Politifact debunks reports that Barack Obama is planning on running for a third term. There are apparently people out there who believe this kind of thing despite the fact that it is legally impossible, there's no way to make it legal in time and that Obama has not lifted a finger to make it happen.
And as Politifact notes, this story was circulated back when George W. Bush and Bill Clinton were in their second terms. I also recall a version that has popped up every time any president, going back at least as far as Lyndon Johnson, was nearing the end of his term. It was that the president and his advisors had whipped up a secret plan to declare Martial Law in the country for some reason — even to stage a bogus terrorist attack here if necessary — and then suspend the election so the Chief Exec wouldn't have to leave. A quick Googling shows that there are currently folks convinced Obama will do just that. I'd say the odds are less than one in three.