I just compiled a quick list of the best apps I have on my Android. Some are really awesome, but I did not put all those installed on my HTC:
AgeTest: it used ultrasounds to test your age. My daughter is 13, it found between 13 and 14. I am 47, it founds 35-40
Alchemy Classics: Another version of Alchemy, very polished
Alchemy Genetics: COOL. Make crazy animals
aTilt 3D Labyrinth: a nice wooden maze with a marble to put in a hole
Blowup: explode house without exploding the panda. Nice physics game
Camel Kitchen: like fruit samurai but you cut fishes and shrimps and chicken instead of fruits
Chalk Ball: a mix between wallbreaker and something else.... You write on a chalkboard to catch the ball.
CubesFree: I cannot pass the 1st level but it is fun, small Android racing in 3D
GeoQuizz: as the name says it
Glassdestroyer: the aim is to destroy pyramids of blue and red glass without breaking the red.
GemMiner: a nice mining game
Layar: a must have for augmented reality
MouseTrap: a very big game inspired from the ancestor Sokoban
Paradise Island: Change a beautiful paradise island in a nightmarish "A-la-Cancun" touristic complex
Realms of Fortune: incredible, a 3D RPG on Android. I just started it, I cannot tell how big it is
Reversi (the one with online option): the offline is very weak but in the online, meet me and lose ! :wink_smile: Seriously, I am pretty wicked at this game and some already regretted it.(I was the 9th best french player in 1986 and I still have some good remains)
SliceIt: a crazy and tough brain teaser. Cut a shape in equal sized pieces with a limited number of stroke.
Spaghetti&Marshmallow: build structures using spaghetti and marshmallows, another physics game
SpacePhysics: a very nice physics game.
Squibble: take the poor squibble out of the labs of the wicked mad man
StarTrader: it is complex but it is REALLY good game a bit like Elite. Incredibly, it is free
Townmen 6: a free strategy game featuring the french revolution. You have to lead your townmen against the troops of the king. Good but you cannot behead the king, it drops the interest.
Untangle Unlimited: the classic Tangle game
X-Construct: Build a bridge for the train. Physics game, VERY tough.
Zenonia: for those who like asian RPG games.

What about the Angry Birds series? Also not really a full game but Androidify is fre and interesting. It is basically an Android paper doll that you can design.

After taking a quick peek at the much neglected 'game' folder, I recommend Guns 'n' Glory, the best I have, it's a western tower defence game.

This is a pretty good list that I will try some out from. I got tired of Angry Birds like six months ago. I don't see why it's all over everything now.

Let's look at my games list...

Andoku - Your basic Sudoku, but better because it can be squiggly.
Battle Ludo - A spinoff on Pachisi, not quite as good but still fun.
Cribbage Deluxe - Speaks for itself
Cyberlords Arcadia - A rather basic but still pleasant RPG experience.
Dice Wars - Simple Risk-like conquest strategy game.
Landrule - Risk, cloned.
Pobs - Clone of one of my favorite old strategy games, Hexxagon.
Shortys - My fiancee's favorite, downloads a glut of crossword puzzles
Tri Tower - One of my favorite solitaire varieties
Wordfeud - Just like Scrabble
ZenDice - Like Yahtzee, but with 6 dice.

I have others, but I haven't gotten around to playing them and can't therefore recommend. Apps I'll do later - in my mind, there's more gems in the apps than there are in the games.

Gurk- 8 bit RPG/Dungeon Crawler. Very fun.
Pew Pew- Twin Stick Shooter. Challenging and fun, with awesome music to boot.
Nethack- Old School Roguelike. Works better if you have a physical keyboard.

Thanks for the recommendations. I have Androify and Andoku. I am already fed up of Angry Birds, but I have it. I also have Gun's & Glory, it is really good, I forgot it in the list. I also forgot Bonsai Blast.

Swords and Earrings, found it today. A strategy game with a story. I played the demo, not sure if $5 is worth it.

Completly new and innovative, I found WhenWho, a very promising app. It makes some data mining in your call history and find the most likely next incoming and outgoing calls with a possible next incoming date.
It is amazing how well predictions are working. It basically tells you who is the most likely person who is going to call you. Presently, my gf should call me in less than 90 min (73% odds), a prospective next employer in 105 min (66% odds) and one friend before 200 min (59% odds).

This is my new, most favorite, thread. Last month I upgraded my phone and decided to go with Big Brother, I mean Google. I've been anti-apple since the 80's and M$ OS just doesn't seem to work properly for phones, so I finally turned my back on Palm and went with an Android. Here's my list of game/apps that I've downloaded. All are 100% free, 'cause I'm a cheap bastard....and some are brand new to me, thanks to the folks who have contributed to this thread.

Air Control Lite - ** - How do they fall asleep with a job like this?
Angry Birds - *** - You know the deal
Angry Birds: Seasons - ** - More of the same, but now with holidays
Angry Birds: Rio - * - Shameless promotion, did the game play actually get worse?
Antivirus - ***- AVG, for my phone
App Delete - * - Boasted that it could delete anything. Lies.
AT&T Code Scanner - ** - Meh, does what it should, but nothing fancy and not popular enough to be useful.
aTilt 3D Labyrinth - *** - Just missing the smell of the real wood game that this is based on.
Chess Free -** - Haven't delved too deeply into it yet, but it seems to be a reasonable facsimile of a chess game.
DanteInferno - *** - Not what I hoped for, but not too bad. Avoid the traps and solve the puzzles. Story included!
Drag Racing - **** - Fun, just mindless fun. Only played it for a bit, but I'll be coming back to it.
Euchre (free) - ** - I love Euchre and this game confuses me. Not happy, but (honestly) I haven't looked for any help file yet.
Geared - *** - I like it, but I have issues with my screen and my thumb. Even with the Off-set, I can't seem to get the gears where I want them.
Hangman Classic - ** - Meh, it is what it is. Nothing special, but it delivers what it says.
HJ Lite - *** - Learn Japanese! I haven't used it much, but what I've seen is pretty cool. It sure beats the ol' paper charts that I used before.
Jewels - *** - Typical flash-type game where you make three in a row.
LaserReflector - **** - Lotsa fun, gets harder as you go.
LOL Cats! - *** - What you'd expect and mandatory for someone with an avatar like mine.
Mahjong Dynasty - *** - Not bad for what it is, but I have that screen to thumb issue again.
Mind Dragon - * - Useless trivia machine...
NetHack - ? - Haven't played it yet. Reminds me of something from way-back, but not sure if it is what I think that it is...we'll see.
Parking Car - *** - Solid. I love this type of puzzle game and get hours of enjoyment out of this.
PDF Viewer - ** - Does what it should.
Pokedroid - **** - Pokedex on your Android! Are you kidding me? Includes Pokemon Black/White.
Pool Master Pro - ** - Not impressed. Physics aren't what I expect (played pool for ages). It's okay for a knock-about game, but nothing serious.
Quest - * - Meh and double-Meh. Must have a network connection, no action, only text-based "quests" (which are auto-resolved). Pass, unless you are in solitary confinement.
Realms of Fortune - ??? - Just got it, thanks to Makandal, but it looks promising!
Replica Island - ** - Not a fan of the "turn your phone to control your character" games. Just seems to have been created to show off the android features, but it's a decent game.
Scrambled Net - ***** - One of my favorite puzzle games! Nothing complex, just flip the pieces to make network connections.
Shortyz - ??? - Correction to Mr.E's post. Not a big fan yet. I love crosswords, but my keyboard seems to take up 90% of the screen and that doesn't help.
Sniper - **** - Pretty solid game.
Spades - **** - AI is a little weak, but pretty good replication of an awesome game.
Star Traders RPG - ***** - OMG, I just got it and it's crack, laced with nicotine and heroine. My wife is looking for you, Makandal!
Texas Hold'em - **** - Very nice, but the ad-delay is really annoying.
Texas Hold'Em - *** - Meh-ish. It's okay, but not great. No annoying ads/delay, but the AI is really weak.
The Rock! - **** - Unless you're a fan and/or from Kansas City, don't bother.
Tricorder - **** - Love it! Maximus Geeksomeus. Turns your Android into a tricorder. It's boring if you anolyze it, but it's awesome if you don't!
Trivia Droid - * - Ugh, why did they bother? Trivia game, but it's as much fun as a visit to the dentist.
Wheel to Riches Lite - ***** - Wheel of Fortune clone and not bad at that. I love it.
Who becomes rich? - * - Lame rip-off of "Who Wants to be a Millionaire?"...and poorly done.
WordTwist - ** - Not what I thought it was going to be, but I haven't ruled it out yet.
ZENONIA Free - **** - Wow! JRPG for Android. Thank you, Makandal!

Bonsai Blast and Air Controller are both good games, except that Bonsai Blast has no replay value once you complete it, much like Angry Birds.

Anyone up for some Words With Friends?

It's basically scrabble over the internet.

Sure, why not? I have to eat dinner in a few minutes but ill go ahead and download it now.

Alright, let me know when you get an account set up.

The only ones I would add are:
Tank Hero - there is a free version and a paid version, the only difference is adds. Basically you drive a tank around 2d maps fighting other tanks based on the weapon given for that map. There is also a survival mode where you get points and use them to purchase weapons and ammo
Rocket Bunnies - best game ever. You play as a bunny in space on a rocketship who must rescue his (or her?) fellow bunnies while avoiding floating debris, bombs, black holes, and the evil bunny-eating spiders. The way you play is kind of hard to describe, but basically you planet hop.
Ninjump - pretty solid game where you are running up two walls and you tap to jump between them. Jumping makes you spin your sword to protect you from enemies. Only problem is that once you are good it stops being fun because the games take way too long
Overkill - another solid game but it is kind of short. You are a space ship thingy and you get to choose and upgrade weapons as you advance. Its really adrenaliney if thats a word, but as I said, the "campaign" so to speak is short and it doesn't have much replay value afterwords.
Zombie Run - Not a traditional game, but loads of fun, especially with friends. It uses the GPS tracker to locate you on google maps. Then you set a difficulty by choosing the zombie speed and outbreak intensity. Finally you choose the safehouse you want to get to. After all of this, it spawns zombies on the map that are always moving towards you and you have to get to the safehouse before they get to you. Super super fun

And thats my list, I don't remember if Overkill is free or not, but to be completely honest, if it isn't free then I wouldn't get it.

Edit: typos are funny
Edit2: I just got realms of fortune and it is great, I highly recommend it!

So I looked up quite a few of these apps and they were paid. Were we trying to discuss ALL good apps or just free?

It was supposed to be free apps but really its hard to say $1-5 is much of a stretch from free.

Just went on an RPG-scouting binge on the market, and found quite a few roguelikes. Of them, one got my attention fairly quickly. Andor's Trail. I expect it will cost money when it's out of beta, but for now it's a decently robust and entertaining RPG that's totally free. I give it my full recommendation. Others that I downloaded but haven't yet tried: Fortunes of War, Legends of Yore, Majesty, and the aforementioned Gurk.

Anyway, I figured I'd continue as promised with some of my favorite apps thus far. Some are standard fare and some aren't:

(A caveat: I'm not the type to root my phone and I haven't yet gotten Tasker, though I might give it a try)

-Notification bar apps: DayWeekBar and Battery Status - gives these stats on the top bar, to accompany the time.
-Cardstar: all those points and rewards cards bulk up the wallet, so I just plug them in here and the Android pulls that duty.
-Dealocrat: I do enjoy Groupon and its kin, but don't exactly like scouring my email inbox every morning for the deals. This app collates all the daily deals for my city.
-Desktop Visualizer and SiMi Folder: both are key for phone customization.
-OnTrack: I have diabetes, and this app makes tracking glucose, insulin, exercise etc a cinch. Also recommended for calorie/carb counting: Personal Dietician.
-Radio Paradise: My favorite internet radio station has a widget. Yay.
-Runkeeper: Seems like a pretty good app for tracking cardio regimens and routes.
-Shush!: Going to see a movie? Silence your phone for only the duration of the movie with ease.
-Stitcher: Gathers podcasts from a plethora of sources for you to listen to.

i needed something like this, i just got an htc aswell