When I first had an iPod Touch and then an iPhone, before the release of the App Store, I had a very hard time wrapping my mind around games for this platform. There weren't many buttons and the idea of controlling everything with the accelerometer just didn't interest me all that much. Currently, I have a few games on my iPhone that I probably would have ever thought to have to my Treo. Here's what I have on my iPhone: 300 Bowl, Cro-Magnum Rally, Motochaser, Spore, Texas Holdem, Aurora Feint, Diner Dash, Top 3 Solitaire, Cannon Game, Koi Pond, and Blue Skies Lite (just downloaded; haven't played it yet). So far, my favorite game is Spore with Diner Dash a close second. I got Diner Dash as a gift for my wife and now I'm hooked!
One thing I learned to do is to put my games on the last page of my menu, that way, I have to go through my programs to get to them. (Will someone please come up with a launcher, or maybe Apple needs to let go of that part of the code.)