Two that come to mind – Daniel Day Lewis is also good actor and Woody Allen, in his free time, makes movies.
Tom Scholz of the band Boston had an engineering degree from MIT and was working for Polaroid while putting together the famous “basement tapes” that were the basis of the first Boston album. He also invented the Rockman line of guitar effects boxes.
Previous thread: Who is the most multi-talented performer currently active?
The winner was Steve Martin, that banjo-playing, singing & dancing, movie writer, director, producer and actor, painting stand-up comedian novel writer.
Other entries included Woody Allen and Hugh Laurie. Speaking of Laurie, I am a huge fan of Ben Elton, who wrote for Blackadder, is a stand up comedian, and also writes musicals and incredibly good novels.
Greg Graffin, lead singer of Bad Religion, said in an interview on NPR that he wasn’t sure how long the band would last, so he ‘didn’t give up his day job’ - he got a PhD at Cornell, and teaches life science and paleontology courses at UCLA. He’s also cowritten two books on religious belief and science.
Oh, and Bad Religion is still recording and performing.
I was going to mention Brian May, too. However, since he’s been taken several times over, I’ll mention another rock’n’roll scientist.
Dexter Holland of The Offspring. He’s a PhD Candidate in Molecular Biology at USC. Looking him up, I see he’s added Licensed Air Transport Pilot, Certified Flight Instructor, and marathon running to his resume.
He also has his own brand of hot sauce.
Alice Cooper is an incredibly good golfer.
Pure awesome.
Brian May has another feather in his academic cap: photographic historian. He co-authored the excellent book of stereoscopic images, A Village Lost And Found last year. It came complete with a stereo slide viewer that he designed.
Marty Robbins was also a NASCAR driver.
Garth Brooks was a baseball player and went to college on a track scholarship.
I wish I could mention Herb Alpert, successful musician, started A&M records with Moss that produced a number of top hits, gives generously to CalArts, and is an accomplished painter and sculptor. But he wasn’t exactly R&R.
Pro wrestler Chris Jerricho is also the lead singer of a band called Fozzy. Jerricho is not known to be a shooter or anything, but still, he’s a pretty tough guy.
Just to add to Brian May’s list of awesomeness: as a teenager, with his dad’s help, he built his own guitar by hand.
Milo Aukerman, lead singer of The Descendants has a PhD in Biochemistry from the University of Wisconsin.
What is it with these punk rock singers? 
Brian Wilson started producing his own work starting in 1962, and produced others. Smokey Robinson was a major producer for all the Motown groups and had his first #1 as a producer with Mary Wells in 1964. Al Kooper left Blood, Sweat and Tears to be an A&R man in 1968 and immediately produced the Super Session album. Pete Townshend produced Thunderclap Newman and The Crazy World of Arthur Brown in 1968.
Notable or innovative? All of these quality. Well-known as musicians? Far, far more than Todd Rundgren, who was an absolute nobody when he first started producing.
By the time he did, which was no earlier than 1969, it wasn’t unusual, different, or noteworthy for a well-known musician to do his own production, or to produce others. It was a standard practice in the rock world. Rundgren isn’t first. He’s not even in the first generation. He’s part of the teeming millions.
Oh, apparently Santini of Sha Na Na wasn’t the only rock musician to go back to medical school.
Paul Arnold, the bassist of the Zombies (“Tell Her No,” “She’s Not There”), also left the music biz and became a doctor.