If you have a Chromecast and you want to try a new app that supports Google's dongle, install TicTacToe for Android or for iOS. It's a very simple game that requires 2 players and displays the results on your TV. You can install it on an Android phone or tablet, on an iPhone or iPad, but you need 2 devices to play the game.
While the game is pretty basic, it shows that Chromecast isn't just for streaming music and video. Once the Google Cast API is out of beta, you'll find a lot more interesting apps. TicTacToe is based on this sample app.