I was thinking about that question too, and I can't think of any really good ones. Ray and Johnny Cash were okay. Part of the problem may be that we see actors portraying artists we know too well.
It's been forever since I've seen Ray but at least those two movies showed or reminded us of their struggles and their flaws.
Documentaries capture the situations way better. For example , I saw one on Amy Winehouse several years ago that was a real eye opener.