I don't buy that many apps in general, so this isn't pulled from an exhaustive list of games I've played. These are just games I stumbled upon, bought for one reason or other, and found myself returning to again and again as I sat in hotel rooms or stayed up past my bedtime on school nights. The list leans heavily on sports-related games, though I'm not sure why...
Baseball Superstars 2009
Play as a pitcher, batter, or a full team as you work your way through season after season in this "cute" baseball game. A 2010 edition is out, but I haven't tried it.
The game that keeps me up at night. A classic match three gems game with great sound effects, my only initial gripe was the lack of integration with Facebook's Blitz version. Once that was rectified, I find I can't stop playing this as I keep trying to top my friends' scores (sometimes to no avail).
Dance Dance Revolution S
I love DDR. At first it seemed impossible that such an immersive game could be made to work on the iPhone, but this version a great job of it.
The Deep Pinball
I love pinball games and I remember playing Night Mission pinball for hours on my Apple IIe (though I could never top the scores my mother posted). On the iPhone, this is my pinball machine of choice.
Fans of 1942 will be right at home with this vertical scrolling shoot-em-up. Using the tilt sensor on the phone, you control a figher plane to destroy the enemy's secret weapon prototypes.
Fastlane Street Racing
While no longer my go-to driving game (that honor goes to Real Racing, mentioned below), I have to give props to Fastlane as my first racing game addiction. It was also the first time I saw the potential for gaming on the device. The only problem was how difficult it was to advance to the next levels. Still, I appreciated it for the beautiful way in which it rendered the landscape and for the accuracy of the physics.
This is the game that took over from Fastlane Street Racing for me. Slightly less challenging game play, but with a greater number of cars and tracks, this is the game that keeps me attuned to the race track.
Real Soccer 2010
A fantastic 3D soccer game, made all the better with a multiplayer option across wifi. The 2010 update makes the game that much more fluid, and actually alters the weather and lighting conditions during season play.
Homerun Battle 3D
Don't feel like pitching or fielding? This game focuses on swinging for the fences. Build up your player as you hit more homers. The option to play against people from around the world is a bonus.
Tiger Woods PGA Tour
Current personal woes notwithstanding, this golf game impressed me with the rendering of the courses and the smoothness with which I could control my player's swing. Once I got the hang of the game, however, it became a lot less challenging. Still, it's a good way to get to the links without leaving your home.