Some very interesting ideas so far. And to think some people say the iphone isn't a mainstream gaming platform...
Seems like a lot of people would like some kind of RPG. So how about a 2D RPG but with a battle system that utilizes game mechanics more native to the iPhone? But something not too arbitrary i guess..
"Battle system that utilizes game mechanics more native to the iPhone" Hmm, well in Final Fantasy 6 one of the characters (Sabin) had a technique called Blitz in which you would have to enter a certain button combination for specific attacks. I'm also reminded of Final Fantasy 10's "Limit Break" in which to increase effectiveness of the attack, a sequence of buttons had to be pressed. Perhaps instead of button combinations you require taps and swipes mixed with accelerometer input, or maybe require the drawing of certain shapes.
so, my suggestion might be a little left field, i'm a big horror fan and there aren't of those options. i'd like to see a 3d maze type game similar to the movie Cube, where some rooms have death traps while others can be safely traversed, and maybe add a puzzle element to unlock doors to the various rooms.