For those saying Doctor Who, I wouldn't really want the Doctor as my medical caregiver. For one, he doesn't seem to have all that much medical experience, and secondly, a lot of people around him die or are put into horrible situations. Just saying.
In on-topic terms of best TV doctor, I'd go with Cox myself. House is so completely unrealistic that, if I saw him or someone like him working as a doctor in a hospital, I'd likely go to a different hospital. One more argument against him that was missed was that he wouldn't mind putting you through intense physical and mental pain just to find an answer. Nor would he really care if you lived or died as long as he found out what was wrong with you before it happened.
Cox, while fairly unrealistic as well I think, is much more realistic about his goals. Yes, he might know that if he's treating you, you'll likely die. He's also more likely to try his hardest to heal you, even getting his army of minions to work on your case as well. Plus I could laugh at his antics with his staff.
Going the really non-realistic route, I think Tony-Tony chopper would be a good one. As others have said, he follows anime-rules for healing. A little rest can pretty much heal anything in those types of shows.