An extremely popular game that now has more players than World of Warcraft.
Although it is free, so perhaps that's not as big an accomplishment as it sounds, but free or not, many people pay money to get skins for their favorite characters. Anything you buy with real money besides skins, you can get with the in game currency as well, so there is no disadvantage on people who don't pay.
The genre is hard to explain, but is a somewhat rare one, known as a MOBA. This means Multiplayer Online Battle Arena. The goal of the game is to fight your way into the opponent's base and destroy their "Nexus". I put it quite simply, but the average game takes around 40 minutes, and has quite a bit to it.
This game has an extremely huge learning curve of anywhere from 2-10 hours for most people, sometimes more. In order to become good at the game, it takes several weeks, although it is more casually oriented.
For those not interested in casual play, this game was featured at Dreamhack
with a $100,000 USD prize pool in June 2011, where several teams fought in competition for the prize.
It is a very fun game, but not something many people can just pick up.
Me: You should totally add Lazukin if you're on the US server and want to play League of Legends.