Many years ago I had the idea that when the 13th Doctor's last season came, he should gain a regenerated Susan or Romana as a companion, train her as his successor, and then in his final moments hand her the TARDIS key and say "You are the Doctor now," starting a whole sequence of 11-12 consecutive female Doctors. I think if you're going to kill off the Doctor and replace him, it's kind of a waste if it's just another man.
Anyway, I don't see how killing off the Doctor would work, certainly not if you replace him with a human as someone speculated. What makes the Doctor so special is his vast experience and knowledge, the centuries' worth of wisdom and trivia he's accumulated in his travels throughout the universe.
Although I suppose they could do something where the Doctor passes on his memories to his successor -- but then it couldn't be a human, or his brain would burn out DoctorDonna-style.