I am gaming on my iPod Touch more than my DS lately. Hope that isn't too blasphemous, but I find the gaming catalog on the App Store to be a lot better than people give it credit for, once you take the time to look for the gems. (This is especially true if you like puzzle games, which I do.) Games in bold are the ones that take up the vast majority of my iPod Touch gaming time.
Frotz - this app includes dozens of the old text adventure games, and lets you download more, and it's free. Totally ****ing awesome.
Aurora Feint II Lite - this takes my favorite falling-blocks puzzle gameplay mechanic (the one used by Tetris Attack/Panel de Pon/Puzzle League/Henry Hatsworth) and adds the accelerometer, letting you turn the device sideways to change the direction of gravity. Add some light RPG elements and nice production values and you've got a pretty addictive title on your hands. Also, free (though there is a more feature-full paid version.)
Bookworm - not much needs to be said here, I just love this game.
Bust-A-Move - pretty good Bust-A-Move version here, though the graphics aren't too great. Anything Bust-A-Move is worth getting imo.
Chuzzle - another ridiculously polished PopCap timewaster.
Drop7 - I may have sunk more into this one than all the other ones combined. Ridiculously addictive puzzle game mechanic. Drop balls that display a number from 1 to 7, and when a row or column has that many balls in a row, they disappear. For example - when you drop a ball onto an existing column of 3 balls, so that the column becomes 4 tall, all the balls with the number 4 disappear from that column - even the ones that were there before. This makes the game very strategic, and the potential for chain reactions is immense. Definitely check this one out.
Earth vs. Moon - a really fun, good looking Missile Command type game.
Eliss - this one is very retro-stylish and unique, but difficult. Uses multitouch well. You have to combine or split apart giant floating circular blobs in order to fit them into holes, but if you let different colored blobs touch each other, you lose health. This one has a lot of style.
Galcon Labs - a really cool strategy game that makes great use of touch. Send armadas of tiny ships from your planets to your enemy's while he does the same to you, take over larger planets for larger regen rates. A lot of different game modes and difficulties, plus multiplayer.
GeoDefense Swarm - the only tower defense game you need (unless you cound Plants vs. Zombies.)
Grand Theft Auto: Chinatown Wars - Rockstar did a great job with this one. I haven't gotten too far into it but the amount of polish and detail is above and beyond for an iPhone game. I'm a little overwhelmed at the possibilities.
Orbital - gorgeous Geometry Wars-esque graphics with Peggle-esque gameplay, really fun. Shoot a ball to knock out other balls, and when your ball stops, it grows in size until it hits another object or wall. Necessitates very strategic aim. Supernova mode lets the balls explode and damage nearby balls, allowing for sweet combos.
Peggle - another great PopCap game. I'm loving going through the challenges on this one. Everyone knows what this is so I won't explain it, but the iPhone version is totally worth getting.
Plants vs. Zombies - can you tell I love PopCap? Just get this.
Space Miner: Space Ore Bust - awesome, awesome Asteroids spinoff, with dozens of zones, upgradeable ships, powerups, different enemy/asteroid types, and really really really funny writing. This is one of the best games I've played in the last couple years, full stop.
Unify - another simple, good looking puzzle game, which has you manipulating two sets of falling bricks at once to match colors. More fun than it sounds.
Zen Bound - this game is truly unique and beautiful. Really nicely-rendered 3D wooden objects that are fully manipulatable about all axes. The goal is to wrap a piece of string around the object - the string covers the object's surface with paint, and you complete each level by covering a certain percentage of the object with paint. You only have a limited length of string, so you need to be conservative in how many twists and turns you use to get into the object's different nooks and crannies. This game takes time and patience, and has a beautiful, serene soundtrack to add to that zen atmosphere. One of the best games on the App Store.