I recommend http://newegg.com for parts. They have excellent customer service, fair prices, good rebates and a good selection. Unfortunately, Newegg only ships to the USA, so if you live in Europe this is not an option. I've never actually used anything other than Newegg, so if anyone has an idea of the best places to order from for Europeans send me a PM and I will update this section.

This guide does not contain any information on laptops. From a gaming standpoint desktops are vastly superior for a multitude of reasons listed below, laptops should only be considered if you absolutely must have portability at all costs. If you have decided on a laptop, you will need to look elsewhere for advice.
Advantages of desktops...
-Cheaper/more powerful
-Upgradable
-Better cooling/airflow
-More customizable
-Larger displays possible

There is tons of good advice out there for actually building a PC, and this guide is more intended to help you with parts selection. Linked below is a great 3 part tutorial series from Newegg TV, which I used myself the first time I built a PC and thought was very helpful. The http://www.gamesas.com/index.php?showtopic=1435536 can also be used to ask any questions related to actually building the PC.
http://www.youtube.com/watch?v=lPIXAtNGGCw - Newegg How to Build a PC Part 1
http://www.youtube.com/watch?v=d_56kyib-Ls - Newegg How to Build a PC Part 2
http://www.youtube.com/watch?v=RxaVBsXEiok - Newegg How to Build a PC Part 3

The Central Processing Unit or CPU is the device which carries out the instructions of the software you are using. It is the brains of your computer and one of the two parts that most determine gaming performance (the other being the GPU). There are currently two companies that are making consumer CPU's, Intel and AMD. Right now, Intel CPU's are superior in performance in the higher price ranges for gaming. The exception would be the sub $175 price range, in which AMD is currently equal or superior. One thing to keep in mind is that all AMD CPU's can be overclocked, while only a select few of Intel's high end CPU's are overclockable. This is the main thing that makes AMD CPU's attractive for budget builds. If you do get an AMD CPU, overclocking is highly recommended.

Another thing to keep in mind is that if you want to stay on the bleeding edge of gaming performance no matter the cost, the Intel i7 platform is actually a viable option, contrary to popular belief. Games are being made more and more to take advantage of hyperthreading, and by the next console generation we could start seeing noticeable gaps in performance between CPU's that can hyperthread and those that can't. In tests of Crisis 3's multiplayer, the i7-2600k gave roughly a 10 fps increase over the i5-2500k. Now, keep in mind that it will probably be a few more years before most games are being made with hyperthreading in mind, so only consider this option if you absolutely must have the top performance in the latest games at all costs.

Overclocking can be done with all AMD CPU's and Intel "K" models. It is highly recommended to do so if you have a CPU that is capable of it. It is generally safe to do if you do some research and understand what it is that you're doing. Overclocking without making voltage changes makes it nearly impossible to damage your CPU. If you do decide to overclock, a CPU cooler is needed. The stock coolers provided by Intel and AMD are not good enough to cool a CPU down under these conditions. For most people, the Cooler Master Hyper 212 or its EVO variant will be acceptable. This cooler costs around $30 and is perfect for those not going for huge overclocks. There are stronger air coolers and closed-loop water coolers, but I don't recommend these. Typically, if the Hyper 212 can't cool the CPU, it's time for a real custom-loop water cooling solution. For massive overclocks, a custom water-cooling loop is what I would recommend, however this can be a lot to think about for new PC builders, so I would just recommend a basic air cooler and then you can later decide if you want to get into water cooling.

Extreme Budget CPU's
These are the bare-minimum CPU's you will need to play modern games. Performance will not be good, but if you must save money at all costs, this is it. Getting anything cheaper than what is listed here will likely result in new games being unplayable. The A6-5400K does not require a graphics card, but the Pentium does, keep this in mind if you cannot afford a GPU right now.
-AMD A6-5400K
-Intel Pentium G860

Budget CPU's
These will be acceptable for gamers who are not interested in maximum performance in the latest games. There is only one CPU in this price range I can recommend, as it beats an Intel i3 pretty severely when overclocked, which is not possible with an i3.
-AMD FX-6300 Vishera

Mid Range CPU's
These should provide great performance in most games and for casual gamers this is the top of the line. If you're not interested in playing the latest demanding games, stop here. The FX-8320 will beat the i5-3470 when overclocked, which the i5-3470 is incapable of. If for some reason you do not want to overclock, performance will be roughly the same between the two with a slight edge to the i5.
-AMD FX-8320 Vishera
-Intel i5-3470

High End CPU's
This is as good as it gets for modern games. Spending any more then this will not net you any noticeable performance gains right now, and for almost all gamers this is the limit on what to spend on a CPU. Only one CPU can be recommended for this range, as AMD is not competitive anymore.
-Intel i5-3570k

Bleeding Edge CPU's
What is recommended here is for those who have no concern for budget. Currently, there will be no noticeable difference in gaming between these CPU's and the much cheaper i5-3570k, however future games such as Crisis 3 are noted to take advantage of hyper-threading in which case these CPU's will be superior. Only pick one of these if you want to stay on the absolute bleeding edge of performance at all costs.
-Intel i7-3770k
-Intel i7-3930k (overkill)

The motherboard is what the rest of your computer's components are connected too, and it is the device that allows them all the work together. Motherboard purchase is done based on what features you need. Cheaper motherboards have less features and functionality, but if you don't need these features, getting a more expensive motherboard would be a waste. Socket type is extremely important, and is the reason I put the CPU section first. You need to know what CPU you will be getting before you decide on a motherboard due to different CPUs having different sockets which will only fit with motherboards of the same socket. For the sake of simplicity, I will only list motherboards with sockets the same as the CPU's mentioned above.

AMD FM2 Motherboards

CPU's mentioned above that are compatible
- AMD A6-5400K

Chipsets
A55 - The cheapest of them all. It is pretty barren, and doesn't have SATA III or USB 3.0 support. It is not likely to have great OC capacity either. I wouldn't bother with these unless you are aiming to build cheap HTPC with minimal gaming capacity.
-MSI FM2-A55M-E33 FM2
-AsRock A55M-HVS FM1

A75 - This chipset has SATA III and USB 3.0 support. Some of these models come with good overclocking capacity too. This is what I would recommend for most FM2 builders.
-AsRock FM2A75 Pro4-M

A85X - This chipset gives you few more ports, RAID support, and the ability to support up to a 4x Crossfire setup. This is just overkill considering the CPU you will likely have to go along with this chipset, and I do not recommend it.
-AsRock FM2A85X Extreme6
-Biostar Hi-Fi A85W


AMD AM3 Motherboards

CPU's mentioned above that are compatible
-AMD FX 6300 Vishera
-AMD FX 8320 Vishera

Chipsets
Only chipsets with OC support are listed here because if you are not overclocking these FX CPU's you are wasting your time.

970 - Most features but no Crossfire/SLI. I recommend these as they are cheaper than the 990FX and this is probably a budget build anyway since it is AMD.
-ASRock 970 Extreme4
-Gigabyte GA-970A-UD3

990FX - Crossfire/SLI support and possibly better overclocking capability. Not recommended unless you are trying to make a performance AMD build.
-ASRock 990FX Extreme4
-ASUS Sabertooth 990FX R2 (overkill)

Intel 1155 Motherboards

All Intel CPU's mentioned above are compatible

Chipsets
H61 - This is the bare minimum budget chipset, and is not recommended unless you must have the cheapest PC possible to get you going. This chipset lacks many features, including USB 3.0, Sata III, Overclocking, and Crossfire/SLI. If none of those features appeal to you, and you just want something to get you going, this is it. H61 boards are not compatible with Ivy Bridge, though some can use Ivy Bridge with a BIOS update.
-AsRock H61M/U3S3
-AsRock H61M-DGS

B75/H77 - These boards offer USB 3.0 and Sata III, but not Overclocking and Crossfire/SLI. I recommend these for budget oriented builds where overclocking is not planned. If you do intent to overclock or try Crossfire/SLI you need to look elsewere.
-AsRock B75M-DGS
-MSI B75MA-E33
-GIGABYTE GA-B75M-D3V

Z75/Z77 - This is the current high end gaming chipset. All features are available here, Crossfire/SLI, full overclocking support and support for more and faster RAM. I recommend these boards only if you have at least an i5 "K" series CPU that you intend to overclock.
-ASRock Z77 Extreme4
-MSI Z77A-GD55
-BIOSTAR TZ77XE4

The Graphics Processing Unit, or GPU is the device that handles all 3D tasks for your PC. This and the CPU are the two most important components that will determine performance in games and a decent portion of you budget should be alloted to purchasing a good GPU. The cards listed here require at least a mid-tower computer case in order for them to fit. Listed next to the card is the minimum power supply wattage that is recommended. This wattage is the minimum for the entire system and has some headroom so you might be able to get away with slightly less wattage but I do not recommend it.

GPU choice comes down to either AMD or Nvidia. Neither company is clearly better than the other, with cards from both coming out on top with different games and price ranges.
A note on Crossfire/SLI. I do not recommend doing this unless you want to have an extreme performance build with a triple monitor setup. For single or double monitors, you will be better off with one high end card than two mid range cards. Crossfire/SLI has some issues currently and I advise against it. It might be something to consider later on down the road when your GPU is showing it's age but not for a brand new build.

Extreme Budget GPU's
These are the bare-minimum GPU's you will need to play modern games. Performance will not be good, but if you must save money at all costs, this is it. Getting anything cheaper than what is listed here will likely result in new games performing very poorly. The only exception to the mid-tower case rule above would be the HD 7750 which is an option below. If you have a slimline case this is your only option.
-Radeon HD 6670 (250W PSU minimum)
-Radeon HD 7750 (250W PSU minimum)
-GeForce GTX 650 (250W PSU minimum)

Budget GPU's
These should satisfy casual gamers and those who do not wish to max out modern games. It is also a good choice to if your monitor resolution is lower than 1920x1080. If this is the case, this is close to the limit of what you need for ultra settings.
-Radeon HD 6870 (500W PSU minimum)
-Geforce GTX 560 (500W PSU minimum)
-GeForce GTX 650 Ti (400W PSU minimum)

Mid Range GPU's
For a single monitor 1920x1080 setup, these cards will provide good ultra settings performance on almost all current games, except very demanding ones such as Battlefield 3. For most gamers, these cards should be sufficient.
-Radeon HD 7850 (450W PSU minumum)
-Radeon HD 7870 (500W PSU minimum)

High End GPU's
This is the maximum almost all gamers will need. These cards will play all current games on ultra with a 1920x1080 monitor at around 60 fps or higher. The 7870 LE card is based off of the same silicon as the 7900 series cards, and is very capable. I consider it the best bang-for-the-buck card in this price range right now.
-Radeon HD 7870 LE (550W PSU minimum)
-Radeon HD 7950 (500W PSU minimum)

Bleeding Edge GPU's
These cards are the best money can buy right now. They are overkill for everything but multi monitor setups and extreme high resolution gaming. Only consider these cards if you absolutely must have the best of the best no matter what the cost. If you want to get a 7970, the GHz edition is not recommended. You can easily achieve the same clock speeds yourself by overclocking the card for free. The Geforce 680/670 are not recommended because they are similar in performance to the HD 7970 but more expensive.
-Radeon HD 7970 (500W PSU minimum)
-Geforce GTX 690 (650W PSU minimum) (overkill)

I'm not going to mention any specific RAM here, but rather give some general recommendations.
-DDR3 is the only thing you should consider and the only thing supported by modern motherboards anyway.
-4 GB is the bare minimum, 8 GB is the maximum. Going lower than 4 GB will have a negative impact on performance and going above 8 GB will make no difference in performance.
-Ensure that the RAM you get is dual-channel for maximum performance. This means instead of 1x8 GB stick get 2x4 GB sticks.
-Ensure it operates a 1.5v for maximum stability.
-Make sure you check to see what speed your motherboard and CPU supports before deciding on RAM. Most modern Motherboards and CPU's support at least 1600 speed RAM, but some still only support 1333. Going above 1600 speed doesn't really offer much in terms of performance even if it is supported, so I just recommend sticking with 1600 unless you have a good reason for it. RAM at higher speeds than what the Motherboard/CPU can handle will still work, they will just be down-clocked to a lower speed automatically.
-Keep in mind that some RAM comes with tall heat sinks that could interfere with aftermarket CPU coolers. You should read some reviews to see if anyone mentions this issue about the RAM before purchasing. RAM without tall heat sinks are fine to use as well.
So if we follow the advice above the most ideal RAM would be 2x4 GB of DDR3-1600 speed rated RAM that operates at 1.5 volts.

Solid State Drives
SSD's or Solid State Drives, are a relatively new item to hit the mainstream computer scene. These devices provide much faster response and boot times then ordinary mechanical hard disks, the tradeoff being much higher price. Because of this, it is usually recommended to get a smaller (120GB-256GB) SSD to keep your OS and some games on and a regular HDD for everything else. You will notice drastically decreased loading times in Windows and all games that you keep on your SSD.
General SSD Tips
-Cheaper SSD's usually are using old tech, so be wary of this.
-SSDs usually come with a Marvell or a SandForce controller. SandForce is known for their speed, but their second generation controllers had caught a lot of flack for being unstable / not working right. Marvell drives are known for being generally, reliable and still performing well enough. Some SSDs come with their own firmware/controller setup, IE) Samsung SSDs.
-Good brands include OCZ Vertex 4, OCZ Vector, Samsung 830/840, Corsair Neutron GTX, Plextor M5 Pro.

Hard Disk Drives
HDD's or Hard Disk Drives, are the most common and widely used form of storage right now. They are much cheaper and larger than SSD's. It is recommended you have one of these even if you use an SSD unless you know you won't be using much storage space, in which case you can get by with just an SSD.
General HDD Tips
-Ensure it spins at 7200 RPM, slower drives are not much cheaper and have a performance penalty
-Do not get the smaller 2.5" HDD's, they have many issues
-Good brands include Western Digital, Samsung, Seagate.

The PSU, or Power Supply is a very important part of your system build. If there is one component you should make sure not to skimp on it's this. Low quality PSU's will not provide the power they say they will, and most likely will eventually die and can take your whole system out with it. In order to select a PSU, you need to know what GPU you will be getting. That is why I listed the GPU section first. Refer to the GPU section above to determine your minimum wattage. I will not list any specific PSU's here, but rather some advice and trustworthy brands.
Here are the brands that you should be able to trust to have a quality PSU
-Seasonic
-Corsair (though I do not recommend the builder series)
-PC Power & Cooling
-Antec
Do not purchase a non 80 plus rated PSU. Make sure it is rated at least 80 plus bronze, higher ratings such as silver and gold are not necessary and do cost a lot so only pick these if power savings are very important to you.
Do not ever use a power supply that came included with a case. These are almost always pieces of [censored] and will likely die and take your investment out with it.

An optical drive is needed by everyone at least to install the OS. Even if you intend to download all your games and other media online, this is a necessary item. Most people will be happy with a cheap DVD burner that costs roughly $20 USD. Any more expensive then this and you are probably paying too much. The only exception would be if you want to play Blu-Ray movies, in which case a Blu-Ray capable drive will be needed. Not much else to say here.

This is largely just going to be based on personal preference, and I won't get too much into cases here. Just make sure that it comes with the features you want, such as front USB 3.0 ports, SSD bracket, etc. And that it has at least 2 fans, one for intake and one for exhaust. Remember that you get what you pay for, and cases are no exception. That being said, I think the sweet spot for a case is probably around $60-$90 for most builds.

Your choice right now is really between Windows 7 and Windows 8. I have no personal experience with Windows 8, so I can't really say if it is better than 7 or not. I've been using 7 for a couple years now and I've been extremely satisfied with it's functionality and performance. The choice is ultimately up to you. Either way, make sure you install the x64-Bit version. I recommend you buy an OEM (Original Equipment Manufacturer) copy for half the price of a retail copy. The difference is that an OEM copy can only be used on one PC. If you ever decide to change your CPU/Motherboard, your copy of Windows is no good anymore. With a retail copy, you can reuse it as many times as you want.

Right now, 1920x1080 is the current standard for gaming monitors. I would recommend this resolution unless you have an extreme budget build with a budget card, then you will be better off with a lower resolution. Good brands for monitors include Samsung, ASUS, and Acer. Ensure that the monitor has at the most a 5ms response time, and 2ms is ideal. There isn't really too much else to say here, and I'm not an expert on monitors anyway.

I won't get into this here as it is largely just based on personal preference, and most people already have this anyway. You can ask in the Community Tech Thread if you want advice about this.

Extreme Budget - For those who just want a PC that can run most games, don't care about graphical quality, and don't have much money to spend. Don't expect much here.
CPU - Intel Pentium G860
Motherboard - AsRock H61M-DGS
GPU - Radeon HD 6670
RAM - Any 2x2 GB DDR3-1333 as noted in RAM section
HDD - Any 7200RPM 3.5" as noted in HDD section
PSU - Any 250W or above
Optical Drive - Any cheap DVD burner
Case - Any mid tower case

Budget - Suitable for those who just want something to game on but aren't too concerned about performance. Also a good choice for those who plan to play on a lower resolution monitor.
CPU - AMD FX-6300 Vishera
CPU Cooler - Cooler Master Hyper 212 EVO (none if not overclocking, you should be!)
Motherboard - AsRock 970 Extreme 4
GPU - Geforce GTX 650 Ti
RAM - Any 2x2 GB DDR3-1600 as noted in RAM section
HDD - Any 7200 RPM 3.5" as noted in HDD section
PSU - Any 400W 80+ Bronze as noted in the PSU section
Optical Drive - Any cheap DVD burner
Case - Any mid tower case

Mid Range - Suitable for most gamers, especially if maxing out all of the latest games is not a primary concern.
CPU - AMD FX-8320 Vishera
CPU Cooler - Cooler Master Hyper 212 EVO (none if not overclocking, you should be!)
Motherboard - AsRock 970 Extreme 4
GPU - Radeon HD 7850
RAM - Any 2x4 GB DDR3-1600 as noted in RAM section
SSD - Any of the 120/128GB performance SSD's as noted in SSD section
HDD - Any 7200RPM 3.5" as noted in HDD section
PSU - Any 450W 80+ Bronze as noted in the PSU section
Optical Drive - Any cheap DVD burner
Case - Any mid tower case

High End - As good as it gets for a single monitor high resolution setup. Will max out anything you throw at it.
CPU - Intel i5-3570k
CPU Cooler - Cooler Master Hyper 212 EVO (If not overclocking don't bother with this build)
Motherboard - AsRock Z77 Extreme 4
GPU - Radeon HD 7870 LE Tahiti
RAM - Any 2x4 GB DDR3-1600 as noted in RAM section
SSD - Any of the 120/128GB performance SSD's as noted in SSD section
HDD - Any 7200RPM 3.5" as noted in HDD section
PSU - Any 550W 80+ Bronze as noted in the PSU section
Optical Drive - Any cheap DVD burner
Case - Any mid tower case

Bleeding Edge - Only consider if interested in multi monitor extreme high resolution setups. This is as good as it gets.
CPU - Intel i7-3930k
CPU Cooler - Custom Open Water Cooling Loop
Motherboard - ASUS Sabertooth X79
GPU - Geforce GTX 690 (SLI if wanted)
RAM - Any 2x4 GB DDR3-1600 or higher as noted in the RAM section
SSD - Any of the 256GB or higher performance SSD's as noted in SSD section
HDD - Any 7200RPM 3.5" as noted in HDD section
PSU - Any 650W 80+ Bronze or above as noted in the PSU section.
Optical Drive - Any cheap DVD burner
Case - Any full tower case. Mid towers won't fit the motherboard.