Last night, the (still technically unreleased) Dota 2 beta registered a peak of 297,000 players. This broke the previous record, set by Skyrim, by almost 10,000, making it the most-played game on Steam by concurrent users in history. With the rate they're sending out free keys, this doesn't really surprise me.
Dota 2 is still a long way from scratching its archrival, League of Legends, who reports active players in the millions at this point. Still, considering the popularity of the Steam platform, it's nothing to shake an Iron Branch at. It's been about a year and a half since the game's soft launch at The International in 2011. League, for comparison, has been around for almost four years, counting from the start of open beta.
Hopefully, this rising popularity will lead to more of an in-person tournament scene for Dota as an eSport, which somewhat disappointingly exists mostly in the realm of online competitions.