Microsoft is going to put out Halo 4 next year, but exactly when Halo 5 and Halo 6 are due out isn't certain.
Love it or hate it, the Halo franchise isn't going away any time soon, even now that Bungie's moved on to other projects with Activision Blizzard. Now that gamers have received a breather from the main series games (with ODST and Reach), Microsoft is returning to the core franchise and has just announced Halo 4 at its E3 press conference.
As you can see from the announcement trailer, the game picks up right where Halo 3 left off, with plenty of action awaiting Master Chief as soon as he's awoken from his cryogenic stasis. Exactly what's going on is pretty vague, other than the ship he's on seems to be under attack and the end of the teaser reveals that the damaged vessel is hurtling towards what looks like a large warp gate.
Halo 4 is due out during the Holiday 2012 season, but that's not all. As Steve Butts explains in his summary of the Microsoft press conference, Halo 4 is the first part of "a [new] trilogy. Bet you did't see that coming."