I've been playing this game called Heroes of Newerth (HoN) since it was in beta. It's based off of the Warcraft 3 custom player made game called Defense of the Ancients (DotA). The learning curve is pretty steep if you're not familiar with the genre, but once you finally get used to it it fucking rules. There's nothing better than making a game with four of your friends and stomping some nubs. Here's a picture of my favorite charactor, Armadon.
There are many amazing videos that teach you the basics, watch one and go play!