Inspired by this thread.
John Lydon. Love him or hate him, his stuff with PiL was way ahead of its time and was hugely influential.
Mike Ness.
Jello Biafra.
Exene Cervenka and John Doe from X. Exene is still playing the punk rock while John Doe keeps it down home and rootsy, but their solo stuff is pretty good. Exene’s recent band the Original Sinners is almost as good as the best X stuff.
Robyn Hitchcock. The Soft Boys are a hard act to beat, but he did pretty good on his own.
Nick Cave
Iggy Pop
Syd Barrett
Bob Mould
Does Joe Walsh count? Or was he solo, Eagles, solo? Can’t remember.
Maynard from Tool. I don’t know if A Perfect Circle counts as solo but it is a different band.
Robert Plant made a couple of good solo albums.
Glen Phillips
Peter Murphy
Chris Bell
Lisa Gerrard
Graham Coxon
And another vote for Syd Barret and Jello Biafra.
And… I’ll probably be largely disagreed with, but he’s a huge guilty pleasure of mine: Morrissey.
Don Henley
Danzig
Stevie Nicks (I think she was in some band or other).
nitro I like early solo Robyn, I lost touch when he seemed to be getting all sensible (the Yip song notwithstanding).
Syd Barrett is an odd case because it’s sort of back to front. The surprise was that PF didn’t suck without him rather than the other way round.
I liked SOME of the early Genesis, but I think the split with Peter Gabriel was good for both the band AND the singer. On the whole, Gabriel has been better solo than he ever was with Genesis, and vice versa.
Perry Farrell. He might have hit the drum & bass tin a little bit late, but ‘Song yet to be Sung’ is a cracking album.
Ice Cube and Dr Dre haven’t done bad.
Chuck Prophet from Green on Red
Bjork
Melissa Auf der Maur
James Gang, Solo, Eagles, Solo. So he counts twice.
Van Morrison after leaving Them.
Danny Elfman
Mark Mothersbaugh
Ozzy Osbourne
David Byrne
Great mention of my favorite, Robyn Hitchcock. I loved the Softboys, but aside from Underwater Moonlight, much of their work was messy and just plain silly. As a solo artist, or with the Egyptians, which is really almost solo he was wonderful. His best works were Black Snake Diamond Role and Fegmania, just after leaving the Softboys.
Bruce Dickinson of Iron Maiden did pretty well when he went solo.
I second that. 
I’ll also add:
Midge Ure (Ultravox/Visage)
My husband introduced me to his solo work, and I’ve come to like it quite a bit.
Steve Winwood
Morrissey
As much as I love and am devoted to the works of Mr Elfman, I would not really call him a solo artist.
His scoring work and musicals are not really “solo artist” type music.
His album So-Lo was actually most of the band Oingo Boingo and only recorded under his name to get out from under a recording contract restriction.
The only vocal work he’s done is the recordings for The Nightmare Before Christmas and that was over 8 years ago.
Nick Cave
Morrissey
Mike Ness
Henry Rollins
Billy Idol - totally eclipsed his work with Generation X
Bjork - much better than her work with the Sugarcubes (althouhg it was good it wasn’t nearly as original)
Brian Setzer
Eazy-E
Iggy Pop
Lou Reed
Shane McGowan
Bands that were as good if not better than the original member’s band:
Butter08 - from Cibo Matto
Foo Fighters - from Nirvana
Circle Jerks - from Black Flag
Cracker - from Camper Van Beethoven
New Order - from Joy Division
Me First and the Gimme Gimmes - NOFX, Swinging Udders, Lagwagon and others
Revolting Cocks - Ministry, and others
Shriekback - XTC, Gang of Four, man many more
Nick Lowe was quite successful as a solo act after Brinsley Schwartz broke up.