I agree that many games from the App Store get boring really fast. I use my iPhone mostly for internet and as an iPod. For my next phone, I would much rather get a phone with a slide-out gaming pad just like the XPERIA Play.
Back when I had a jailbroken iPod touch, I had hundreds of ROMs. I had a NES, SNES, Genesis, and GBA emulator. The prob was it sucked playing with touchscreen controls and I only played NBA Jam or Deal Or No Deal.
I had over 24+ games on my iPhone 4 but filtered it down to just 12 now which includes mostly puzzle, tower defense, and racing games. It is a solid dozen of games that I can always go back and finish. I basically picked up a bunch of $.99 games when they were on sale last Holiday season which would normally cost $2.99 or more. I even had Madden but hated the controls and deleted it. My fav game playing on an iPhone is sill Plants vs Zombies. I can still play that from time to time but it can be very easy. And Field Runners was the first game I ever liked from the App Store and I still keep it on my phone for sentimental reasons.
My current fav is ChuChu Rocket which I got last November and the game started from the Sega Dreamcast. I will play that for 30-45 min sometimes about 2-3x per week. After I finish ChuChu Rocket, I will probably get into finishing Angry Birds, Cut the Rope, and Pee Monkey Plant Bloom. If I am not playing ChuChu Rocket, I sometimes play Monopoly (which cheats) and a free Chess which is timed. But ChuChu Rocket keeps my mind sharp. Hundreds of levels. Thanks to Sega on how to make a real game that I can spend hours and feel I accomplished something meaningful. I don't feel that with Angry Birds which can so difficult and becoming too commercialized or a game like Doodle Jump which feels less rewarding.