The Sims Social
The Sims Social game has become very popular on Facebook by making players find new friends and build social relationships.
you can invite your friends and add them as your neighbor in the sims world and perform some of the daily tasks which you do in your real life.
Words With Friends is a simple and interesting game by Zynga which has brought Social gaming to Facebook with games like FarmVille and Mafia Wars.
you can challenge your friends or play with a random opponent and you can buy useful addons to make the game more interesting.
Tetris Battle needs no introduction as it is a widely played electronic game,this game can be played by two players at a time.
Uberstrike is a Multiplayer First-person shooter which is made with unity3d,If your GF is a fan of action games then be sure to play uberstrike.
Draw My Thing from OMGPOP is an excellent game to tell something by drawing on the screen and the other player guess the name of the thing you have drawn.
Keep playing wonderful games on Facebook and send us links to more interesting games that you discover so that we can add them to this list.