The Beach Boys on Full House.
Bonnie Raitt on Roseanne (I think, right?)
Eddie Money on The King of Queens
Sammy Davis Jr. on All in the Family
The Dillards on The Andy Griffith Show
mmm
Willie Nelson on Monk
Frank Sinatra on Magnum PI
Jefferson Starship on The Star Wars holiday special
I won’t even pull up any 90210 bands
That was Bonnie Bramlett (Delaney & Bonnie) seen here with David Crosby.
http://www.youtube.com/watch?v=NIxqqwJ3Kp0
Oh yeah, I knew it was a Bonnie. 
Anyway, THIS is the scene, starting around 3:48, that I still remember from seeing it “live” all those years ago. Day-um!
mmm
Jon Bon Jovi as a housepainter on Ally MacBeal. One of the better decisions the show made was that Ally didn’t end up with him.
Bon Jovi also has appeared on 30 Rock, as NBC’s Musician in Residence.
I have a vague memory of Yoko Ono on Mad About You.
Thanks for the memory jogger. Along the same lines, Absolutely Fabulous had a number of music stars appearing as (fictional) versions of themselves - Lulu, Marianne Faithful, Suzi Quattro, etc.
Warren Zevon on Suddenly Susan, Dream On, and Larry Sanders.
Reverend Horton Heat on The Drew Carey Show.
A whole bunch of people on 30 Rock. According to Wikipedia (This is just from the Kidney Now episode):
Clay Aiken
Sara Bareilles
Beastie Boys (Mike D and Ad-Rock)
Mary J. Blige
Elvis Costello
Sheryl Crow
Steve Earle
Wyclef Jean
Norah Jones
Talib Kweli
Cyndi Lauper
Adam Levine
Michael McDonald
Rhett Miller
Moby
Robert Randolph
Rachael YamagataMel Torme appeared several times on Night Court.
Also on Home Improvement as Wilson’s cousins.
My nomination:
Bell Biv Devoe on Fresh Prince of Bel Air.
Huey Lewis has appeared on Just Shoot Me, One Tree Hill, King of Queens, and Hot In Cleveland.
DeBarge was mentioned in the first post, but not for his appearance on the Gil Gerard/Ernie Reyes Jr. show Sidekicks.
Uh oh, I posted that Eddie Money was on King of Queens, the episode I was thinking of was Huey.
Although there was one episode involving an Eddie Money concert; I’m not sure if Mr. Money was actually on the show or not, though.
mmm
Jon Bon Jovi also did a guest spot on Las Vegas.
Michael Des Barres played Sir Charles Weatherbee (“Call me Dog.”) on WKRP In Cincinnati.
And Mick Fleetwood was on TNG–not that you could tell it was him under that alien makeup/mask.
You got it right. Eddie Money was on KOQ. Doug wins some money but he has to spend it before Carrie finds out. They keep buying stuff but just can’t burn through it, so they run into Eddie Money and hire him to sing in Doug’s living room.
Debbie Harry of Blondie has done a bunch of acting and TV appearances. Too many weird ones to list them all, but I note she was a character in the pilot for Sabrina, the Teenage Witch (ugh). As herself on Ab Fab, etc.
Her most embarrassing listing is being musical guest on Pink Lady a.k.a. Pink Lady and Jeff. One of the most ill-conceived TV variety shows of all time.
(Both Debbie Harry and Pat Benatar from my first post appeared in the movie Union City, btw. Yet another worthless thing my brain has decided to store.)