During BlizzCon, Blizzard announced that they were looking at getting Hearthstone into open beta by the end of 2013. Sadly though, an update posted on their blog shows that this won't be possible.
We believe the right thing to do for the game is to not rush it out into open beta, but to instead hold onto it a little longer to make sure it’s ready for wider testing.
Due to this push back of the date, Blizzard also announced that they have sent out beta invites to everybody that opted in to the Hearthstone closed beta prior to December 16th. It is still possible for you to sign up to the closed beta test, however, this is not guaranteed to enter you. You have until January 7th to get your opt-in checked, as this is the date that they close.
Welcome to all new players and we hope to see the rest of you on the tables soon!