I’m a big fan of the (now defunct) Japanese band Kagrra,. One of their guitarists also played a Japanese string instrument called a Koto (as in this song Uzu).
I remember Brian Jones of The Rolling Stones played the marimba in “Under My Thumb”, and John Entwhistle of The Who played the french horn.
Are there any other bands where one of the regular musicians plays a non-traditional instrument, both in the studio and live?
Thanks in advance.
(p.s. the bands name has a comma at the end 
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Several bands have had flute players, including Ian Anderson of Jethro Tull, Ray Thomas of the Moody Blues, and Greg Ham of Men at Work.
The Beach Boys used a Theremin.
Well, there’s the cowbell in (Don’t Fear) The Reaper.
It’s a Beautiful Day featured a violin-playing front man, David Laflamme.
Lyle Lovett’s Large Band features a cellist.
Thanks to Gravity’s frontman (Andy Happel) plays violin as well. (they’ve disbanded, but were great).
Ashley MacIsaac, plays a fiddle most of the time (except one album) and sometimes does traditional celtic music, but sometimes does rock and roll.
Tanzwut is a metal band with a bagpiper.
Apocalyptica plays metal on 4 cellos.
The E Street Band had saxophonist Clarence Clemens as part of their line-up. A lot of rock bands have brought in an occasional saxophonist but few have one as a regular member.
From that same generation, how about George Harrison’s sitar in “Norwegian Wood” (studio work).
Martin Barre also played marimba for Tull.
David Bowie’s “Space Oddity” features a stylophone.
The mid-'70s band Sailor regularly used a keyboard instrument of their own invention, that they called the nickelodeon.
Curved Air featured Darryl Way’s electric violin.
And, of course, the Velvet Underground had John Cale on viola.
Cleis Pierce played an electric viola in the art-rock band McKenzie Theory.
Almost every member of Gentle Giant played instruments unusual for rock music, including recorder, “Shulberry” (3-string custom electric ukulele), vibraphone, xylophone, mandolin, clarinet.
Frank Zappa and his bands of course have played almost anything, including a bicycle.
Juicy Lucy featured a steel guitar played by Glenn Campbell (no, not that Glenn Campbell) very much in a rock style, very different from the way it is more traditionally used in country music.
The Doors, most unusually for a rock band, did not have a regular bass guitarist. Although they used a session bassist in the studio sometimes, when live (and I think on some studio tracks too), organist Ray Manzarek would play the bass line on a Fender Rhodes piano bass (whilst playing the other keyboard parts with his right hand).
The Bonzo Dog Band had members playing the euphonium, trumpet, tuba, harpsichord, banjo, spoons, accordion, tap dancing, slide whistle, and a trouser press.
The Lovin’ Spoonful often had John Sebastian on autoharp, at least on some of their TV performances.
Otis Taylor plays blues, but often includes a cello and a banjo in his songs.
The Who also wanted a cello for “A Quick One While He’s Away,” but since none of the band played one, they sang, “cello, cello, cello, cello, cello.” 
And while Springsteen was one of the last groups to have a saxophonist, they were very common in early rock: the Dave Clark Five, for instance, had one.
and theremin leg. 
Morphine:
Two string bass, tritar (bass string and 2 guitar strings), baritone and bass saxophone.
The Presidents of the United States of America
From Wikipedia:
The Dropkick Murphys also use a bagpipe.
If you’re thinking of “Good Vibrations,” technically it was a “Tannerin” or “Electro-Theramin.” Here’s what it looks like. It’s different enough (IMHO) to point out the distinction.
Burton Cummings played the flute in the Guess Who classic “Undun”.
The Canadian band Saga had a member who sometimes played the clarinet.
One of the original videos to air on the fledgling MTV was by a band called Art in America, which had a harpist.
And of course, there’s accordionist “Weird Al” Yankovic.
The New York Rock & Roll Ensemble featured members who played oboe, English horn, cello, trumpet, and French horn.
Ian Anderson plays balalaika on several tracks on the album Stand Up.
The swarmandal is used on several Beatles songs.
On “Alabama Song”, Doors keyboardist Ray Manzarek plays a marxophone.
The clavioline is featured on Del Shannon’s “Runaway”, the Tornados’ “Telstar”, and the Beatles’ “Baby You’re a Rich Man”.
The Troggs’ “Wild Thing” includes an ocarina solo.