As you might imagine, my iPhone is more littered with games than useful stuff like Steve's or Victor's. Sure, I've got Twitterific and NetNewsWire, but my most-used apps are of the video game variety.
The game that's most grabbed me so far is Aurora Feint. When it was first released, I didn't get much out of it, but since it's been updated a few times, Aurora Feint has turned into a pretty deep puzzle/RPG. There have been some security scares, unfortunately, and the game's "MMO" promises haven't yet come to fruition. But for sheer matching puzzle gameplay (it's similar to the great Poker Smash on Xbox Live), it's probably the most addictive game on the App Store.
My second favorite is Characters (I originally wrote about it on WoW Insider). If you play World of Warcraft and have an iPhone, this is the closest thing you'll find to an official Blizzard app. It lets you see every bit of information on the Armory in a very nice-looking iPhone app format. We're still waiting on Blizzard to provide us with an iPhone version of the in-game Auction House or mailbox, but until then, this is a great way to look up the WoW characters of folks you meet.
And finally, I've been really impressed with Midomi (and also the similar Shazam), a music recognition app. Hit the app, let it listen to a song you're hearing (or even you singing the song or saying the lyrics), and it'll tell you exactly what that song is. And once you've find it, you can listen to it, find it in iTunes or on Youtube, or see band pictures and reviews. Midomi is the kind of app I've never had on any other devices I've owned, and yet I've put it to great use a few times.
Honorable mentions go to Freeverse's (renamed) Moto Chaser, which is consistently the game that most impresses people playing with my iPhone; Trism, which turned out to be an excellent game, and Frotz and Sketches, both of which I've written about here before.
And I'm still waiting for two things: some great persistent pet gameplay (Wil Shipley, what happened to all of those ideas?), and some great location-based MMO gameplay as well. There's good stuff out there, but we're still just getting started in the App Store.