Here are a couple with a musical theme that I would add to my list:
Sid And Nancy (Chloe Webb as Nancy Spungen and Gary Oldman as Sid Vicious) is a classic. I just did a google and Courtney Love had a part that I do not remember, but seeing as how it was about junkies, I am sure she was convincing.
Georgia starring Mare Winningham as the vocally talented Georgia Flood, and Jennifer Jason Leigh as her younger sister, Sadie Flood, who is either of lesser talent or perhaps, in my opinion, talented in a different way. Sadie has demons, that's for sure. And that's an understatement. The movie also features Ted Levine (whose acting I really enjoy) as Georgia's partner, John C Reilley played in the group with Sadie (I think he was the drummer), and Max Perlich played Sadie's boyfriend for a period of the film. This film completely won me over the first time I watched it, and it was one I watched a few more times.