[Update: it appears as if only the tutorial is now available for newcomers without a key, with the rest of the game to come at a later date. If you need a key, I'm sure you can easily get one in the comments below.]
Fresh off of the announcement that Dota 2 will be fully "released" this summer, prospective fans can now play the game without a beta key. As Patrick pointed out, since Valve has provided hundreds of keys to every single Dota 2 player (of which there are a ton), odd are you have had zero problems getting a key.
But for the two or three of you who couldn't get their hands on one, feel free to boot up Steam and just log in the game as normal. The only real difference is the fact that the intro plays before the game starts, so don't expect anything massive, as the game still isn't technically out yet.
Dota 2 activated on Steam [PCGamesN]