I've seen a lot of topics posted here and elsewhere on how to raise ____ skill quickly. Well, I will post it here. This is all current as of patch 1.8.

Combat Skills:

Smithing -
Use the fortify restoration loop to make a ridiculous fortify smithing potion. Then upgrade an item; it doesn't matter what. For example say an iron dagger. Using the smithing potion made from the fortify restoration loop I made a dagger that did well over a 100,000 damage I think. As such, the value was through the roof. Remember how Bethesda made smithing progress in regards to value of item? Bingo. Go from level 1 to 100 with one upgrade. This is even faster than making 200 iron daggers to achieve the same result.

Heavy Armor -
Equip Heavy Armor and go to a giant camp and let them beat on you. Heavy/Light Armor is raised based on strength of attack hitting you. Nothing hits harder than two giants. You'll get to 100 in about half an hour.

Block -
Same principle as Heavy/Light Armor. Go to a Giant camp and tape your left trigger/Block button and go eat cereal. By the time you're done with the cereal you'll be at 100 in block.

Two Handed, One Handed, and Archery -
No quick way. These are the only three I can't really find a quick way to level.

Light Armor -
Equip Light Armor and go to a giant camp and let them beat on you. Heavy/Light Armor is raised based on strength of attack hitting you. Nothing hits harder than two giants. You'll get to 100 in about half an hour.

Sneak -
Find an essential NPC. Equip two non upgraded iron daggers and up the skill to master if it isn't already so. Double sneak attack the NPC. Rinse and repeat until level 100.

Lockpicking -
Amass an assload of lockpicks. Go to a master lock and tape your left joystick (XBox 360) to the left or right so that it automatically tries to pick a lock and break. Repeatedly. This takes time. Go somewhere else while you're doing this. Read a book, watch a TV show, or something.

Pickpocket -
Reverse pickpocket about say 700 or 800 gold onto someone. Pickpocket it back. Reverse pickpocket the gold back and steal it back. Rinse and repeat. Real easy. This will take about 10 minutes to get to 100.

Speech -
Remember that ridiculous dagger you made to get smithing to level 100 in an instant? Sell it to a merchant. You're now at 100 speech. Congrats you cheating bastard.

Alchemy -
That fortify restoration loop you were doing to make a potion to smith a ridiculous dagger? Chances are, you got alchemy to level 100 while making a fortify smithing potion with ridiculous stats to make said dagger. If not, abuse the fortify restoration loop to make high value potions. Will literally take two minutes to get to level 100 this way.

Illusion -
Enchant some gear to to give you 100% illusion spell cast reduction. Don't have your enchanting leveled up to do so? It's ok, use the fortify restoration loop to do it. Keep in mind you're going to need to do this for every school of magic to level it up quickly.

Cast muffle on yourself over and over.

Conuration -
Kill something. A rabbit, chicken, hell, even a mudcrab. Cast soul trap on it repeatedly.

Destruction -
This is a pain, I'll admit. Just remember the higher damage the spell does the faster it levels. Beat on Shadowmere for a while. Hope you have a turbo controller so it'll cast by itself. If not, your fingers will hurt.

Restoration -
Same as destruction. It's a pain.

Alteration -
Go into the center of town where there are many NPCs. Dual cast Detect Life and tape the triggers down so you can walk away. Come back in about 20 minutes. Alteration will be at level 100.

Enchanting -
A pain but made easy via the Dawnstar Merchant Chest. Make sure that the Khajiit trader that goes to Dawnstar is currently there. Go to the chest and take ALL soul gems. Run to the merchant and save. Attack her. Reload game. Her inventory and thus her merchant chest will restock. Run back to the chest and steal all soul gems.

Rinse and repeat until you have about 200 soul gems. Now make 200 iron daggers. Enchant them all. You'll be at level 100 in enchanting. It's easier than it sounds and isn't as time consuming. Dedicated about an hour and some change for this particular skill.

Fortify Restoration Loop Exploit is ridiculously powerful. Ridiculously powerful. I would recommend players to stay away from it, unless you want to ruin your gaming experience.

Of all the exploits that are available in this game, I would say this is most egregious.

But I imagine there are some players out there who enjoy being ridiculously OP. Well, have fun guys. But make a save game and make note of when you start using this exploit. And make note of how long it took for you to abandon the character.

I agree. I don't use any potions made via the Fortify Restoration Loop. Only when I was trying to level up skills AFTER I did everything in the game. But the information is there for people who want it.

Actually, you know what? I just lied. Early on in my game I made a necklace and ring who had the following stats:

Necklace - Alteration and Destruction Magic 81% less magic to cast
Ring - Illusion and Restoration Magic 81% less magic to cast

Add that with the benefit of being a Necromage Vampire the active effect is 101% reduction in Alteration, Destruction, Illusion, and Restoration. Therefore, from the very beginning 4 out of the 5 schools of magic didn't cost anything for me to cast.

Then again, magic is severely under powered compared to melee and that's how I justified it.

Scuse me for asking, but what is the fortify restoration loop?

Well, there are times where it is helpful. Since Silver can't be improved, one would need to use the resto loop to make it viable. However, 9/10 times it will make you incredibly powerful if not used in moderation.