Games that support DualShock 3 controllers are appropriately marked.
TowerFall Full game: $14.99, supports DualShock 3
This simple 2D multiplayer game pits up to four players against each other in a deadly bout of bow-and-arrow combat. You kill other players either by impaling them with an arrow or stomping on their head. The battlefield is littered with power-ups and multiple paths, forcing players to concentrate at all times, lest they get an arrow in the back or a crushed skull.
BombSquad 1-8 players, Full game: 4.99, supports DualShock 3
Hidden in Plain Sight (2-4 players, Full game: Pay what you want $0.99 - $49.99, supports DualShock 3
Hidden in Plain Sight began life as an Xbox Live Indie Game back in 2011, and now it's one of Ouya's most entertaining multiplayer games. There are several game modes, all of which involve players trying to blend in with NPCs to achieve a specific goal. "Ninja Party" for example, fills the entire screen with duplicates of the same ninja character. First, you have to figure out which one you control. Next, you can either touch five special statues or eliminate the other players. If you make your character too obvious though, the other players may just eliminate you. This is a great game for casual players, and even those who aren't playing will have fun watching.
You Don't Know Jack (1-4 players, Full game: $10, supports DualShock 3)
Another caveat, you'll need an internet connection to access the full game. If the network is disconnected for any reason, the game reverts to the trial mode.
BombBall (1-2 players, Full game: $2.99, Supports DualShock 3)
BombBall is 2D game that sits somewhere between air hockey and Pong. Players fight for control of the ball and try to fling it into the opponent's goal. Power-ups add some variety to the mix, with traps that boost player speed or launch the ball in a specific direction.
Super Crate Box (1 player, Full game: Free, supports DualShock 3)
No Brakes Valet (1-2 players, Full game: Free, supports DualShock 3)
Get On Top (2 players, Full game: $1.99, supports DualShock 3)
A port of QWOP creator Bennett Foddy's physics-driven wrestling game. Two players are connected at the hands, and each can jump, push or pull in order to topple the other. If your head hits first, it pops right off and you lose. Like Foddy's other games, it's stupidly simple and completely hilarious. Also, if you need to settle an argument, it's the best thing since Rock, Paper, Scissors.
Polarity (1 player, Full game: 4.99)
A first-person puzzler in the vein of Portal, Polarity puts players in the role of a hacker stealing data for clients. Set in a spartan virtual world, you'll flip switches, carry cubes and launch yourself over ramps to reach each level's goal. You can also shift your polarity between red and blue at any time. Switch your polarity to blue, and you can step on red walkways. Switch it to red and you'll fall right through. This leads to tricky puzzles that require you to shift polarity mid-jump later in the game. It's a bit on the short side, though more levels are being promised.
Like You Don't Know Jack, the purchased version of Polarity shifts back to the trial version if you lose your internet connection.
Emulators (Players, prices and controller support varies)
I know that many prospective Ouya owners were hoping the device could serve as an easy solution for playing classic and homebrew games on a television. Based on my limited testing, it looks like the console will serve that role very well. Note that emulators are located in Ouya's "Retro" section, not the "Apps" section.
Knightmare Tower (1 player, $3.99)
One of my favorite games from the Ouya Kickstarter launch in March, Knightmare Tower is a simple, one-button game. As a dashing knight, you rocket into the sky, slashing downward as monsters come from underneath. Slash enough of them to get a boost, launching your way up the tower and saving princesses along the way. Between sessions, you can purchase upgrades to your weapon, armor and rocket. It's easy to play and bizarrely addictive.
And, of course, all the games I highlighted back in March are still available as well. The Ouya library is a little short on deep, engrossing single-player experiences right now, but there are still many enjoyable games to be found, especially if you enjoy local multiplayer.