The rumor stems from a poorly translated interview regarding final fantasy 13, in which the developer mentioned that "the fate of final fantasy XIII is under serious consideration."
They were talking about the numberings of the games at the time that the comment was made, so they may have been talking about dropping the number at the time and giving it a subtitle. They could have also been referring to it moving to the PS3 or staying on the PS2. Or they could have meant that FF13 would be a massively overhauled Final Fantasy. They did not, and have subsequently confirmed, that the series isn't ending at or after 13.
I wish they would start a new mainstream RPG series though. We need a truly mainstream, massive, non-niche RPG that carries its own legends and NONPLAYABLE elements and over into each game while keeping the game itself an independent, novel play experience. I'm sick of Star Oceans and Tales games to the point where I don't even bother with the 2nd-class RPGs. I'm sick of Zeldas where each new game is just a sad mod pack you pay full price for. The only things I pick up nowadays are DQ, FF, and original new titles in hopes that they will become a new MAINSTREAM series. Playing to niche groups who play their "unique" game because no one else does has killed the heyday of the RPG.
So yeah, the FF13 being the last one was a myth that's been going on around for about 2 years.