1984 by Eurythmics (altho the director tried to stop the use of any of this music, and later denounced their involvement, the music is terrific)
200 Motels by Frank Zappa (who also concieved the film and wrote parts of it)
Hi, Opal!
Dune doesn’t count because Brian Eno supplied one of the themes in addition to Toto’s work.
Also, I’m not sure where Peter Gabriel’s soundtracks to Birdy, The Last Temptation of Christ, and Rabbit-Proof Fence fit in, since they kind of bridge the gap between score and song-based soundtracks.
Curious George Movie - Jack Johnson
True Stories is all Talking Heads/David Byrne, even though most songs are performed by members of the cast.
Magnolia’s a particularly good example since PT Anderson was listening to her while writing the screenplay and wrote specific scenes around specific songs, and then she wrote some original songs for the movie.
Though Garden State’s soundtrack is made up of different artists, it is worth noting that Braff wrote the screenplay around certain songs and attached a mix CD to the script when he was shopping it around (cite). That’s how come there’s that remarkably silly line about The Shins in there.
Tom Waits and Crystal Gale collaborated on the entire soundtrack to One From the Heart.
Belle and Sebastian did the soundtrack for Storytelling, and Air did The Virgin Suicides.
Dave Davies of the Kinks scored Village of the Damned, and wrote one song for the score of In the Mouth of Madness.
I was thinking that Enya performed all the music for the BBC’s television documentary The Celts, but this implies that she only supplied some of the music. (Yet she has an album titled “The Celts”) 
Yeah except for the two Supertramp songs, one by Jon Brion, and the one by Gabrielle.
My contribution is the score to the movie The Virgin Suicides, which is by Air. This is confusing, though, because the soundtrack is one of those indie artist collections. So again this doesn’t really count.
Bjork contributed the entire soundtrack to Dancer in the Dark (she also starred) and another movie called Drawing Restraint 9, which, IIRC, was by her husband. The Tosca Tango Orchestra did the music from Waking Life which is song-based, in an instrumental way.
I’ve always been partial to the cover of that movie’s maritime anthem Tug A-Hoy! by Jack Dean Tyler and the 4 Skins.
Danny Elfman scores most of Tim Burton’s film, and a few others…
…Dave Dobbyn did the soundrtrack for the movie Footrot Flats: A Dog’s Tail, which sadly, most of you would never have heard of before! There are some samples on the link, Slice of Heaven and You 'oughta be in Love are quite simply Kiwi Classics…
It doesn’t quite match the OP, because the artist was dead at the time, but The Sting uses Scott Joplin rags exclusively for its soundtrack.
Badly Drawn Boy did all the songs for the movie About a Boy.
nope. Storybook Love was “Written and Performed by Willy de Ville”.
Kenny Loggins and Caddyshack!
Pink Floyd did the entire soundtrack for The Wall, I believe.
Ok, kidding around. But they did do the soundtrack to “More”.
Easy Rider was by Steppenwolf
Trivia: Pink Floyd were going to do the soundtrack to Jodorowski’s Dune (as a double album!) before he was dropped from the project.
I’d like to point out that what you hear in the movie doesn’t always make it onto the soundtrack, and vice-versa. One example of this is the movie Valley Girl. The Plimsouls have about a half dozen songs in the movie, but only 3 show up on the soundtrack. Also, sometimes you’ll hear like 5 seconds of a particular song in a movie, but the whole song appears on the soundtrack.
Prince did all the songs in Batman.