League of Legends
An action real time strategy game. Each team has 5 players, each with a different champion and the objective is to fight your way into the enemy the enemy base and destroy their nexus. Each team has waves of npc minions spawning that rush towards the enemy base and fight anything they meet on the way, you can kill these to earn exp and gold to buy new items to improve your character. This stuff is vital to winning but it resets each game. Its much deeper than I can describe so you should check out some videos if you're interested.
Alien Swarm
Top down coop shooter. Its entirely free, there's no store or anything. There's 4 classes, medic, commader, tech, and special weapons. You level up to earn new weapons and equipment. The campaign that comes with it is fun but pretty short, there are quite a lot of community maps and missions though.
I didn't know that was free now! I lost my disk ages ago, must get!