I came in here specifically to mention him. I love 30 Seconds to Mars.
Steve Martin is an accomplished banjo player.
His wife, Jada Pinkett Smith, fronts a metal band called Wicked Wisdom.
Yeah, a metal band. http://www.youtube.com/watch?v=p1g6viZ3DEw
Ice T was a famous rapper.
Cher.
I came in to mention how wonderful Milla as a musician is, and also the very fine Minnie Driver, but too late.
Toni Collette is in a band with a terrible name called Toni Collette and the Finish.
:dubious: She has a long and interesting filmography beyond that. If nothing else, see the Before Sunrise and Before Sunset before judging her acting abilities. See Sunrise first or else Sunset won’t make much sense.
Musician/Actor? That’s easy. It takes real talent to be an accomplished musician, a major Hollywood actor, and an NBA All-Star all at the same time.
Why, yes, I did type that with a straight face. Why do you ask?
What, no love for Kareem?
John Schneider, of Dukes of Hazzard & Smallville fame, had a fairly successful career as a country singer.
I just realised we’ve missed the grand daddy of all actor / musicians
Frank Sinatra.
John Corbett of My Big Fat Greek Wedding is a musician as well.
Post #39, The Second Stone got him, but it was easy to miss.
Wasn’t Bob Hope a sometimes song-and-dance man, too?
If you count singing Thanks for the Mammaries, then yes. 
(Hope did sing, but his musical career wasn’t anything to write home about. He didn’t have a bad voice, but seemed more interested in acting than singing.)
How could I forget Gene Autry or Roy Rogers, the singing cowboys of yesteryear?
Sissy Spacek is primarily known as an actress, but I have a very decent album she made, and of course she did all her own singing as Loretta Lynn in Coal Miner’s Daughter, and was even nominated for a Grammy (Best Country Vocal Performance, Female). Btw, her daughter Schuyler Fisk is following in her footsteps singing-wise.
Speaking of Coal Miner’s Daughter, Beverly D’Angelo did her own singing as Patsy Cline in the movie and did a damned fine job. According to her trivia page at IMDB, she toured Canada as a singer, and fronted a band called Elephant.
[nitpick for The Other Jeffrey Lebowski] It’s Aimee Mann.[/nitpick]
Harry Connick, Jr.
Yummy.
Sometimes – many stage musical comedy stars (like Hope, Ethel Merman, James Cagney, etc.) went on to act in films, but are really known as actors.
There are also people like Hoagy Carmichael and Lyle Lovett, who did a reasonable amount of acting, but who are best known as musicians.
OTOH, Steven Van Zandt is probably best known to the general public as Sylvio Dante in The Sopranos and not for his long stint backing Bruce Springsteen.
TV actor Alan Thicke is also a composer of TV game show theme music.
Michelle Pheiffer did her own singing in The Fabulous Baker Boys, and she was very damn good.
Kevin Spacey did his own singing in his Bobby Darin pic “Beyond the Sea” and released an album full of Darin songs.
Well, there was that flash in the pan named Presley, too, if we’re counting that sort.