I seem to have a penchant for loving games on my HTC EVO 4G that can't be won. Perhaps this is due to being a kid when games such as Pac Man and Galaga were new, where the only goal was to survive as long as humanly possible.
A Game With Balls is something of a cross between Missile Command and Space Invaders. The object is to protect your cannon from wave after wave of various sized balls that want to fall on you. You accomplish this by shooting bullets and cannon balls to deflect the menacing spheres (and occasionally other shapes) away from colliding with your cannon. Objects react in different ways when hit with your ammo. Some move slightly, some fly straight up, some get heavier, etc.
The game consists of four infinite levels, each of which has to be unlocked by scoring points in gameplay. Each has its own shapes, gameplay, music, and cannon that accompany it. All are visually appealing, but I'm about 50/50 on the music.
A Game With Balls is $0.99 in the Android Market, and you should be able to tell within the refund period if it's your type of game or not.