The Doctor has fared a whole lot better than some of the other aging timelines we've seen recently. I guess that's one of the perks of having a Rassilon Imprimatur in your police box. (Jokes for nerds!) Watch the all new season premiere of Doctor Who tomorrow, April 23 @9/8c, only on BBC America.
(As many have pointed out, the Face of Boe is actually Captain Harkness, but given that this is what someone looks like when they get really, really old in the Doctor Who universe, we'll stand by this as a reasonable "And Beyond" approximation.)