As of 2012, they're still on the 11th; he'll have to regenerate two more times before there's a 13th.
In some stories (both TV and otherwise), we've gotten some hints and foreshadowing about future Doctors, but that's it.
The reason the 13th Doctor is (or will be) significant is that Time Lords only get 13 lives, and everyone's curious how they're going to keep the Doctor alive (and keep the show going) after his 13th incarnation dies. There are many possibilities, but fans love to argue about things like which of those many possibilities the writers are likely to use.
The other reason the 13th Doctor is significant is that current show-runner Steven Moffat's first Doctor Who-related work was a parody called The Curse of Fatal Death, where the 13th Doctor was female. Whenever people speculate over whether/when we'll get a female incarnation of the Doctor in the real series (as opposed to a parody, or a what-if story, etc.), people bring that up.