As Boroda said, President Putin is currently only allowed two terms in office.
As an interesting aside, I was here (St. Petersburg, Russia) for New Years, and right before midnight, President Putin addressed Russia on television screens throughout St Petersburg (and, as I assume, the rest of Russia). The thing I found most interesting (as an American) was that everyone in the crowd was actually paying attention to what he was saying; as well as cheering.
Oh, and Russian politics are VERY interesting (if you're into that kind of thing).