The best I have seen so far is "And the Band Played On". It's a film about the AIDS epidemic in the mid 80's and the researchers involved. The thing that I liked most about the film was that they looked at the disease from multiple points of view - the patient advocacy groups, gay rights activists, researchers, etc. Also the portrayals of the researcher personalities were fairly accurate for a movie. Awesome movie, very touching too.
Another movie was "The Doctor" with William Hurt. It was based on a true story of a surgeon who developed throat cancer. The film is about his transformation from a cold, impersonal doctor to a kind, compassionate one. The movie is a little bit cheesy and overdramatized at times, but still pretty good.
I liked "Awakenings" as well, although they exaggerated and overdramatized a lot.
If you're into Kurosawa films, '''Redbeard" is pretty good. It's kind of like a samurai film and doctor film rolled into one. It's about an intern who is forced to practice medicine in a village. Initially, he is disdainful of the villagers and country folk, but under the tutelage of Redbeard, played by Toshiro Mifune, he becomes passionate about treating the underserved. Kurosawa also made the film "Ikiru" which I didn't like so much, but has received a lot of critical acclaim.