Depends on what you would call "outsider" music. A lot of people think of "outsider" music as constituting music from people who were aiming for being pop stars, but totally failed and ended up appealing to a fringe market for "strange" music. So I see the term, in that sense, as having to do with historical context rather than music as such. And people like Tiny Tim, Derek Bailey, and Captain Beefheart arguably wouldn't fit - they made strange music, they seemed to know they were making "strange" music, and they didn't care.
It's possible that aspiring pop stars that were really "underground" artists like Daniel Johnston and R. Stevie Moore count as outsider music. That said, a lot of what they make really counts as successful pop music to me, especially Daniel Johnston who at times is too straightforward for my liking. Wesley Willis, again outsider music. The Shaggs, yes. The Residents, maybe, depending on what their intentions were at the beginning. Jandek, I doubt it, despite the tag. Some people I haven't seen that would count include Kenneth Higney, Gary Wilson, and Jack Mudurian.
Some "outsider" music I dig (albums and songs):
Daniel Johnston - Yip-Jump Music
R. Stevie Moore - Phonography
Gary Wilson - "6.4=Make Out", "Loneliness", "Dream(s)"
Complete - "Hoogie Boogie Land", "Beatiful Sunrises" (sic)
The Shaggs - Philosophy of the World, especially "My Pal Foot Foot"
Kenneth Higney - Attic Demonstration
Some "strange" and/or lo-fi music I like that may or may not be "outsider" music, but is superficially similar to some of the above:
The Fall - a lot, but especially Dragnet and Hex Enduction Hour
Tim Buckley - Lorca, Starsailor
Neil Young - Tonight's the Night (not avant-garde at all really, but then neither is most of Daniel Johnston's music)
Syd Barrett - both of his albums
Flipper - A lot, but especially Album: Generic Flipper
Jandek - a lot, but especially Ready for the House, Chair Beside a Window, and Telegraph Melts
Captain Beefheart - Trout Mask Replica, Lick My Decals Off, Baby
Royal Trux - Royal Trux [1], Twin Infinitives
Ween - GodWeenSatan, The Pod
James Chance and the Contortions - Buy
The Residents - a lot, but especially Meet the Residents, Not Available, and Eskimo
John Frusciante - Niandra LaDes and Usually Just a T-Shirt