Whenever I see folks posting about their favorite OUYA games, I see the same names come up again and again are Towerfall (a nice enough game, but I think you really need four players to make it shine), BombSquad (which is fun, but I suck at it), and Amazing Frog (which must be getting reviewed by people on much stronger medications than I am).
What I never see mentioned is The Ball, which is a shame, because I think it's the best game I've seen on the platform so far. This is a port of a PC game, and it's likely that the PC version has better graphics and tighter controls, but I thought it worked quite well on the OUYA. It's a first-person puzzle game, where you are running around a subterranean complex, overcoming obstacles and smashing mummies with the help of a giant rolling metal ball.
Aside from this massive sphere, your only tool for solving puzzles is a magic artifact that you can use either to pull the ball toward you from any distance, or to push just about anything away from you. The "push" feature only works at point-blank range, so if you're hoping to use it to knock mummies around, prepare to get up close and personal.
I was constantly surprised and pleased at how much variety they got out of just these simple tools. The game is a long series of challenging puzzles, with a few action sequences thrown in to keep you from getting too complacent. (Thankfully, there were very few jumping-platform puzzles, which I detest with a passion.)
I think this is a must-play for anyone who liked Portal. The Ball doesn't have Portal's humor, and the storytelling isn't as strong, but the puzzles are solid and there's plenty of them.
My only problems with the game were the unresponsive jump button (there was a noticeable lag between hitting the jump button and actually jumping, though this could have been an OUYA controller issue) and the final puzzle, which was a fairly tedious trial-and-error thing (and I will gladly send the solution to anyone who wants it; I solved it on my own mostly due to a few lucky guesses).
There are plenty of fun little arcade games on the OUYA, but The Ball provides a more long-term, immersive, and thoughtful experience, and was well worth my $10.