Now coming in January 2014
Bad news for those of you who wanted to play Hearthstone as soon as possible without an invite -- Blizzard has delayed the open beta until January 2014. Blizzard notes in a blog post that they don't want to rush the game, and want to be double sure that it's ready for wide testing.
If you opted into the beta before December 16th however, they're apparently sending "everyone" invites, so check your spam folder if you haven't gotten one yet. The opt-in for the closed beta will end on January 7th, until the open one begins. So yeah, get on that! Hearthstone is pretty fun for what it is.
Hearthstone Update - Open Beta [Battle.net]