Alright, everybody, take a seat; I've got this.
If the Doctor remains male, my candidates would be (In order of preference):
* Craig Charles (The ultimate smeghead becomes the ultimate smeghead with a much cooler, yet still just-as-somehow-busted ride.)
* Sir Patrick Stewart, a man whose credentials as a science-fiction authority figure who specializes in diplomacy are indisputable.
* David Tennant. Yes, David Tennant. We still have Ten's half-human clone running about. If something Permanent were to befall the original Doctor, the halfie could regain full Time Lord biology using the Chameleon Arch, and bring Rose with him again. Could get interesting if they run into River again.
* Sir Christopher Lee, a man who is, quite frankly, the ultimate badass given his name and the fact that his life and ancestry are a gigantic heavy metal album. Could also get a new Sonic Screwdriver with the same rough shape as Count Dooku's lightsaber as a friendly reference. :)
* Richard Hammond. Any time I see David Tennant wearing anything but a suit that Ten would wear, I can't shake the feeling I'm looking at Richard Hammond anyway. :)
If we're getting a female Doctor... Again, in order of preference:
* Catherine Tate. Yes, Catherine Tate. Donna still has the DoctorDonna personality and memory matrix within her, just suppressed. Again, if something Permanent were to happen to the Doctor as we know him, it might happen within eyeshot of Mrs. Donna Temple-Noble, thus restoring her DoctorDonna memories and personality. And as for the "burn you up" problem, that's simple; she can use the Chameleon Arch to make herself biologically a Time Lord.
* Georgia Moffett. Yes, Georgia Moffett. Jenny is, notionally at least, still at loose in the universe. If something Permanent were to happen to the Doctor, the TARDIS might seek out his next-of-kin; his daughter Jenny. She might take up the mantle of the Doctor in place of dear old dad. Plus, that would make her the Doctor's Daughter who married the Doctor and had the Doctor's Daughter and then became the Doctor, which is just convoluted enough to work. (Not to mention it would make David Tennant the Doctor who married the Doctor's Daughter and sired the Doctor's Daughter whose spouse then became the Doctor.)
* Amanda Tapping. Basically, Dr. Helen Magnus IN SPACE AND TIME! That couldn't possibly be anything but hilarious!
* Sigourney Weaver. Why not? Her science fiction chops are indisputable, and Avatar proved she can technobabble with the best.