One of my favorite iPhone games is "Mega Jump". It really is a game made with this platform in mind.
In the game you control a character by tilting the phone from left to right. The character jumps higher and higher the more stuff it collects. I love the simplicity of the controls. Many games attempt to be like PC games and have dual virtual joysticks, but that doesn't really work well. In Mega Jump there is no need to touch the screen at all during the game. I love the graphics too. As you can see it has that "cel shaded" feel to it, solid colors with thick black borders.
The game would be just fine as it is and pretty successful too I think, but what really sets it apart is how it entices the player to come back. You play it a few times, and just when you're about to get tired it unlocks something for you. You see, every time you play you get kind of experience points, and these unlock new levels, bonuses and characters. So when you return to the game, it will have something new in it to try, even though the gameplay itself is as simple as ever.