You're in for a treat with this one -- Bit Pilot is a dual-stick shooter without any actual shooting. You guide a tiny little ship around a screen while asteroids and various obstacles float past you, and try to stay away from trouble for as long as you can. Shield powerups also float by, but over time, of course, things get tougher and tougher, until you're frantically trying to dodge everything the game tosses your way.
The ambient feeling of this one is where the real brilliance comes in -- some awesome music and really amazing pixelated graphics sell the concept perfectly, and I love how the game basically unlocks itself as you play it. Like Tiny Wings, another really solid one-man title, different modes and goals open up the more you play, so there's always something new to find, unlock, or aim for.
Zach Gage's Bit Pilot is an excellent title, and well worth the buck. It's universal with Game Center integration. I'm going to say this one is a must-have, no matter what kind of games you enjoy on Apple's touchscreen devices.