Dota 2 is on Steam, and is a petty good free team-based game, but it can pretty much be summed up as a multiplayer RTS. If you've ever played anything like League of Legends or Heroes of Newerth, it's basically the same type of game.
Speaking of League of Legends, you can probably tell that a large amount of people on the forum play it, so you could get a few friends to play with (which helps a lot in MOBA games, especially if you're starting out). It's not on Steam, but it is free to an extent; you're required to purchase characters, with real money if you choose, but they can all be gotten through playing regularly.