Probably either Sudoku (not really exclusive to iPhones) or Unblock Me. P: I'm boring when it comes to games, hah.
I haven't gotten to many but at the moment my favorite game, if you call it one, is Dragonvale. I love dragons ;~;
I think my favorite iPhone game is either Unblock Me or Temple Run. I recently began to play 100 Floors, but it keeps making me mad because the puzzles aren't self-explanatory enough. Sudoku and Draw Something aren't bad ones either, I just don't play them as much as I used to.
WINTERBELLS. WINTERBELLS WINTERBELLS WINTERBELLS WINTERBELLS. Clean design, catchy music (+bonus points for strong flavors of Pachelbel's Canon in D), and simple & addicting gameplay have made this one of my favorite iPhone games ever since getting it in November. I still play it consistently after all this time. I think part of it is that I don't really play games with big storylines or fancy mechanics on a tablet or phone -- I want something I can just pick up and play. It was originally a free Flash game on Orisinal but it made the transition to iOS really smoothly. Downside is it's not free on the app store :c it's 99 cents, but imo well worth it.
Not a big fan of iPhone games, but I did enjoy playing this air hockey game (forgot what it was called though)
774 Deaths! The only iGame I would play just because it is the ONLY Nanashi no Game ever localized! x_x And of course there is still Higurashi: When They Cry Ep1, Ep2, Ep3, and Ep4. There is Still Higurashi: When They Cry Kai Ep1 (my favorite btw). Oh and how could I forget Silent Hill: The Escape! :D Try all of these out <(^o^)>