And of course, after I posted this, I remembered that Travolta also acted and sang in musical theater and cut a couple of record albums. But that was a long time ago.
But I think either Lumpy misunderstood the OP or I was whooshed.
He’s right.
flees
Kevin Spacey recently completed a 10-year stint as artistic director of the Old Vic in London.
Think of how short the list is of famous puppeteers. And then think of Frank Oz doing Bert-and-Ernie comedy routines – or Kermit-and-Fozzie ones – with Jim Henson; and think of his Yoda up on the big screen, and his Cookie Monster on the small one.
Also, he’s directed well-received movies that have nothing to do with puppets. So really think about that: you’re watching a British film like Death At A Funeral, and then you see it was directed by the guy who’s the best there ever was at doing the voice of Miss Piggy? You liked Dirty Rotten Scoundrels, and then found out it was directed by the one true Grover? (Okay, that one makes perfect sense, but still.)
The point is, one has nothing to do with the other; he’s just that good.
Fred Gwynne, star of Car 54 Where are You? and The Munsters, was a cartoonist for (and president of The Harvard Lampoon and also asuccessful author and illustrator of children’s books.
If we can define art as show business, Ronnie Wood, guitarist for the Rolling Stones, has a second career as an artist, whose works have been very well-received.
Dwayne “the Johnson” Rock. Biggest star of pro wrestling during it’s biggest boom period to major box office draw.
Hulk Hogan, Roddy Piper, Jesse Ventura all tried, but didn’t have nearly the success.
But Ventura was successful in politics, and after that has tried his hand at being a professional nutbag.
And the recently deceased Chyna went from wrasslin to starring in another type of “movie”.
On to non wrestlers, Fred Grandy went from acting on the Love Boat to elected office, and Sonny Bono went from singer/entertainer to elected office.
Louis C.K. successfully transitioned from standup to “Louie”, his sitcom on FX, which he created, writes, produces, directs, edits, and stars in. Talk about all hats.
And he still finds the time to do standup.
I guess politics can be considered a kind of show business for some. 
Lee Strasberg was the guru of method acting. He was almost completely known as an acting teacher until near the end of his life when he took some high profile acting jobs like Hyman Roth in Godfather 2.
Someone on the previous page brought up politicians long before I did. Something about show biz for ugly people or something, but I don’t know that I’d call Ronald Reagan or Fred Grandy ugly.
It’s not uncommon for an actor to later become a director or producer, but the other way round is rarer.
John Houseman first became famous as a producer on both Broadway and of movies, notably Citizen Kane, before becoming an Academy Award winning actor, and later acting on TV.
Otto Preminger was a famous director who later had a few acting roles, including in Stalag 17 and Mr. Freeze on the Batman TV show.
Alfred Hitchcock of course was famous as a director, and did uncredited cameos in most of his films. However, he is probably most iconic as the host of Alfred Hitchcock presents on TV.
If they do, then Bob Uecker had an acting career, starring as George Owens in the sitcom Mr. Belvedere.
Paula Abdul started as a cheerleader for the Los Angeles Lakers, where she was discovered by the Jacksons, who asked her to become their choreographer. She went on to choreograph music videos and directed the giant piano keyboard sequence in Big. She later went on to fame as a popular recording artist.
I was thinking that Travolta essentially had two separate movie careers, unless that doesn’t count for this thread.
His early career was when he was barely out of his teens, so he was almost like one of those child actors who couldn’t get work as an adult, but then suddenly he could, once he gave up on heartthrob roles and started taking character roles. The reason that Travolta “counts,” I think, is that a lot of people thought he was a one-trick pony-- he was all looks and dance moves, and once he got older, he wouldn’t have a career, but he is turning out to be a very versatile character actor.
ETA: Barry Williams had a lot of trouble finding work in Hollywood after The Brady Bunch, but finally settled into a career in the theater.
Jackie Gleason composed/arranged/conducted more than 50 albums of vintage 1950s lush, romantic music, although there’s some controversy about how much beyond the basic ideas he actually brought to the table.
Il Duce wrote Romance novels. A little off-topic, but too good not to mention.
Queen guitarist Brian May completed his PhD in Astrophysics in 2008 (he had left off on his studies in the 1970s, when the band took off). While music is still his primary career (and Queen has been touring in recent years, with Adam Lambert), he now has a sort of secondary career, mostly in England, as a celebrity scientist. He’s appeared on several TV astronomy / science shows, and co-written a book on the history of the universe.
If someone makes the point that all that was still “acting” for Steve Martin, one should mention that Steve Martin has nowadays gained critical acclaim for his musicianship.
Impressive. He can talk to Stephen Hawking on a completely different level than a good many of the test of us.
John Travolta went into a critical and box-office slump in the 80s, but he had steady work. His filmography shows that he’s averaged one movie approximately every two years, including the three Look Who’s Talking movies with Kirstie Alley before Pulp Fiction came out.