Milla Jovovich and Scarlett Johansen have both released albums.Jovovich's(Divine Comedy) is quite good, sort of Kate Bush meets Bowie in a folk club feeling.Johansen's(eponymously titled) is not impressive at all.
According to the interviews on the DVD of Walk The Line,Phoenix did do his own singing despite what imdb says.
John C Reilly does his own singing and playing in Walk Hard.
Someone mentioned Lorne Greene of Bonanza fame.He had a single in the UK charts in the early 60's named "Ringo" but whether you could call it singing is arguable.I would say he recited it as he did with the b-side the Bonanza theme.
Minnie Driver's 2 albums are worth a listen if you like contemporary singer/songwriter material.