The "online team brawler" Heroes of the Storm has been offering beta sign-ups for quite some time now. First things first, though: the game needs to hit alpha. Blizzard is inviting "a very limited number of players [in the United States, at first] to join us in an initial phase of infrastructure and technology testing that we're calling the Technical Alpha."
The so-called "core experience" has been realized, however this Diablo, Warcraft, and StarCraft mashup title is "still very much in the early stages of development."
Express your interest in participating by opting in on the Beta Profile page of your Battle.net account; if you're selected, Blizzard will send you an invite via email. Some members of the press are being granted access as well and there won't be a non-disclosure agreement in place, meaning once the alpha goes live, expect to hear a lot about the game.
Introducing the Heroes of the Storm Technical Alpha [Heroes of the Storm]