Jool (stylized as JOOL on the App Store) is one of the most inventive games I've seen in a long while. It's an endless running game, which in itself is not inventive. And unfortunately, the game isn't all that intriguing -- you basically just run as a character horizontally along the screen, jumping up and falling down a series of platforms while trying to collect all sorts of crazy objects.
But here's the inventive part: When your character finally falls off of the bottom of the screen, you can flip the iPhone upside down, and your character will automatically flip into a different character running the opposite way, giving you a chance to keep your run going. It's a wild little gimmick, and it's crazy to see in action -- just when you think your character is done for, you can instead flip the phone over and keep going. There are a few other gameplay elements, like bombs that will propel you forward, and occasional goals for certain items to collect, but that "flip" is the wildest thing, a really crazy idea that's implemented in a wild way.
Unfortunately, the rest of the game isn't nearly as impressive: There's a very weird "loading" feature that makes you just sit there and do nothing while files download when the game first loads up, and the graphics are more goofy and confusing than really supportive of the gameplay. But Jool, in all of its awkward weirdness (the game was made by four artists from Berlin, if that explains their somewhat twisted sensibility) is worth a try just for that strange flipping feature, probably the most inventive way I've seen the iPhone's accelerometer used. It's available for 99 cents from the App Store now.