John Stamos was on “General Hospital” and played drums on tour with the Beach Boys before “Full House.”
Lloyd Grossman was in a punk band in his youth.
(although I doubt that too many on the US side of the pond know who he is)
Robbie Rist (“Brady Bunch”, “Big John/Little John”, “Battlestar Galatica”) has been a guitarist/songwriter/vocalist for several bands (The Andersons, Wonderboys) and currently plays with The Mockers. They just had a couple of Top 40 singles in Spain within the last year (“The Empire Stricks Out” and “Dejame”.)
And ** audiobottle**, I have an autographed vinyl of Bruce Willis’s LP The Return Of Bruno. He sang and played harmonica on it. A lot of Mitch Ryder-esque rock. Not bad for an actor.
Not that he’s in a rock band, per se, but Steve Martin is a very talented banjo player. Had a hit song, too.
And Minnie Driver apparently has a very nice voice - she’s recently put out an album, but I hear it’s not really doing that well.
This doesn’t quite fit the OP, but Sammy Hagar has made more money by making tequila than he has made in music.
There’s Henry Rollins.
If you’re a fan of the early 80’s punk scene or the 90’s buttrock scene you’d know him for his music.
A lot of other folks know him from his small roles in a number of movies: Johnny Mneumonic, The Chase, Heat, Bad Boys II, Lost Highway and many more.
He’s also been a big ol media whore in TV with a few acting roles, some hosting duties (full metal challenge and night visions), and soem voice work on cartoons and video games.
He also runs his own publishing company that releases his albums as well as other people’s and books by several authors.
Oh yeah and that spoken word thing.
Phillip Taylor Kramer the bass player for Iron Butterfly became well known as a rocket scientist.
He then became famous for his disappearance and the subject of X-files-like conspiracy theories.
Then he was a skeleton found in a ditch.
I saw Ann Magnuson at the old AMOK Bookstore in L.A. about three-four years ago. We were both looking at a book John Gilmore’s book on Manson & she said “I don’t know why I look at this stuff” as she looked. L
Anyway, she asked the manager if she could leave cards advertising her show & he said something like “Sure, Ann, you know you’re always welcome to.” So after she left, I looked at the cards… for Bongwater.
I asked the manager “Was that Ann Magnuson?” Him- “Yeah.” Me- “From the sitcom ANYTHING FOR LOVE with Richard Lewis & Jamie Lee Curtis?” Him- thinking “Yeah, I guess so.” (That obviously wasn’t what he first thought of regarding her work.)
SO that was my unwitting brush with greatness. If I only realized…
I might be Mr. Magnuson now!
(Now someone’s gonna tell me she’s gay & dash my dreams L)
Johnny Depp moved to L.A. to be a rock singer, not an actor. He still plays and sings with his band at Viper Club and other venues.
The girl from The Wizard is the lead singer of Rilo Kiley?
No wonder I like them.
“He touched my breast!”
“What breasts? She dosen’t have any breasts!”
Just three or four years ago? I thought Bongwater broke up over a decade ago, with Magnuson and her partner, Kramer, feuding bitterly.
In Finland, he definitely is a household name. The Bold and the Beautiful is the soap opera, only bested by Salatut Elämät, a homegrown soap. Any visits by BtB stars are considered big celebrity events, and Ron Moss (or rather, ‘Ridge Forrester’) is even the subject of a minor pop music hit.
Anna-Lynne Williams, the female vocalist and songwriter of trespassers william was *Employee of the Month * at the Claremont, Ca Borders last year! 
Jack McDowell, who was 127-87 with an ERA of 3.85 in 12 seasons as a pitcher for the White Sox, Yankees, Indians and Angels, was another baseball player/musician.