Brink game is a beautiful first-person shooter, in which your hero is trying to survive on the Ark - a set of little islands, that saved the humanity from the death. Brink game is a unique shooter, because it is focused on the parkour-style movement. There is an online mode in the game, where you can play together with people or fight against them.
If you like actions with parkour-style movement, try Assassin's Creed III. If you like first-person multiplayer games, you should download Battlefield 3. And another interesting work from the same developer is Doom 3.