If you like to draw you will love Draw Something. It is a non competitive game that you can play with your friends or random players. You download the game for free but there are in App purchases available to give you more colors or bombs. It is easy enough to play the game without having to resort to in App purchases.
Basically one person draws from a choice of words and then it goes to your friend to guess the word for what you have drawn. One thing I think is fun is that you get to watch your friend drawing as it records the process rather than just showing the finished result. Watching someone draw is half the fun of the game.
If your friend guesses right they get a certain amount of coins. You can spend your coins on color packs or bombs. Bombs are used to get a new set of letters or special words that offer more coins.
You can connect with your friends on Facebook. I have also played with random players. I think you can also sign up with out facebook but it is really easiest to just connect through Facebook.