We don't see many games that allow you to play between iOS and Android devices. However this one does. Fun Run is a great multiplayer racing game. It is incredibly addictive. Get it from the App Store or the Play Store for free.
When you first download the game, it will ask you to register. By the time you finish, you will be able to play the game online. You can either play randomly with other users, or you can add friends and play with them. In other words, no Game Center needed.
The game's idea is pretty simple, you control a running animal by jumping and using weapons you collect on the way. It looks a lot like Crash on the Playstation. Anyway, it is a great game that you should defiantly check out.
By the way, if you want you can add me, my username is: amabd95