I am a HUGE fan of Biopics myself, I think it's interesting to see a real person being portrayed by an actor whether it's an actor they are portraying, or a writer, etc...
Of the latter day biopics, on particular favourite of mine is Richard Attenburough's "Chaplin" from 1992. Although there are quite a few error's as to some character's and events in Charlie's life, Robert Downey Jr did a superb job as Charlie Chaplin, and it was a delight to see Geraldine Chaplin (Chaplin's daughter) play her real life Grandmother. Although I was always a fan of Charlie Chaplin, the biopic was a good way to introduce Charlie's movie's to my friend who otherwise would probably have never watched his silent films.( I am a HUGE Charlie Chaplin fan so that is another reason)
Another movie which I think was rather good, was Martin Scorsese's "The Aviator" . I thought Leonardo DiCaprio did a great job as Howard Hughes, who was definitely one of Hollywood's most interesting stars. What was also great about the film was the fact that it exposed a side of Howard some people may not have known. Personally I did not know much about Mr. Hughes passion for aviation and how he really was an inovative and important part of the aviation field. The battle between insanity and brilliance stands out.
I shall probably come up with more as I love biopics but I thought I would start with those, hehe