This Sega classic was born to be on the iPhone. It uses the iPhone's accelerometer to determine the angle you're holding the phone; rather than using a boring old joystick or D-pad to move your little monkey-in-a-ball, the action of tilting the phone tilts the floor surface.
Be warned that it's hugely difficult. The accelerometer is either very sensitive or just not very good at reporting its position back to apps; either way, navigating AiAi round tricky tracks takes real skill and patience.
It's a wonderfully big game; it feels like a proper console game, and so it's a bargain at £5.99.