The sax hook is like the most well known part of Harden My Heart, so it’s fun to know that the lead singer is also doing that. It’s got to be a lot of work though.
Is Frank Zappa a “lead singer”? He played non-traditional instruments, including a bicycle.
Yeah, but he didn’t sing along when he played the bicycle. 
John Linnell, They Might Be Giants, plays the accordion.
As does Van Morrison.
Pete Townshend is credited with “Jew’s harp” on Join Together, but only backing vocals.
The Guess Who’s Burton Cummings learned to play the flute specifically for the instrumental sections of “Undun.”
So does Flea of the Red Hot Chili Peppers, although I don’t think he sings.
I once saw a “Behind The Music”-esque show about them which included an interview with Flea’s junior high band director. When Flea entered 7th grade, not only was he a shoo-in for first chair, he called his parents in for a conference. They probably thought, “Okay, what did Michael do THIS time?” but it was to tell them that he was far and away the most talented student he’d ever had in class. Who was in second place? Another trumpet player he’d had in his first few years of teaching, Herb Alpert.
Lead singer Lady Aïcha of Fulu Miziki bangs on some pipes in this video.
One of the two lead singers of Gaelic Storm, Patrick Murphy, plays accordion, spoons, and occasionally bodhrán. The other, Steve Twigger, mainly sticks to guitar but I’ve seen him on bouzouki and mandolin.
(Speaking of unusual instruments, the group’s piper, Pete Purvis, plays a few different types, including an electronic bagpipe, which is a total trip.)
Also saxophone.
Mike Love (of The Beach Boys) has played what Wikipedia calls “rudimentary saxophone.”
Blue Oyster Cult’s Eric Bloom gained some notoriety for playing the mysterious “Stun Guitar”. (as far as I know he did not play cowbell)
He knows two whole notes…
Johnathan David of Korn plays the bagpipes
Got ninja’d on a couple of these instruments, but just had to mention that seeing John Sebastian live blew my mind.
I’d grown up with elementary school teachers (with no musical talent) trying to play the classroom autoharp. They’d manage to play chords, awkwardly holding down the plastic bar labeled “C”, then “F”, then “C” again, to such rockers as “Jimmy Crack Corn” or “Mary Had a Little Lamb”, all at a slow-yet-off-tempo pace.
To see “Summer in the City” and “Do You Believe in Magic” being played on an ELECTRIC autoharp was so cool. The man redeemed a despised instrument for me.
You may be interested in this YouTube channel. He deconstructs stuff including the Lovin’ Spoonful, breaking them down into the individual tracks. Summer in the City includes garbage can. He has them live in 1965 doing Do You Believe in Magic and You Didn’t Have to Be So Nice with Sebastian playing autoharp. Lots of Who too.
Thanks, cool site!
Mark Lindsay of Paul Revere and the Raiders played sax. It was featured prominently on some of the early recordings, but later on he pretty much only used it as a prop.
I haven’t seen Jacob Collier mentioned. He is a solo performer who plays multiple normal instruments and sings, but his showpiece is playing his own voice as a polyphonic instrument using a harmonizer.
He also has a nice line in playing the audience as an impromptu choir.
Only on one song I know of (“Pea” off One Hot Minute, which is basically a comedy song AFAIC)