The Corrs (specifically Caroline Corr) played the Bodhrán on a number of tracks.
In Moxy Früvous, Jian Ghomeshi occasionally played the tin whistle.
Shoehorn With Teeth, by They Might Be Giants, used a glockenspiel.
Andy Mackay of Roxy Music sometimes played the oboe (as here in Virginia Plain).
I think that is Grace Slick playing a recorder on Jefferson Airplane’s “Comin’ Back to Me”.
(Possibly it is a flute. My ear is not good enough to be sure. However, she is holding a recorder on the album cover. On the other hand, though, the cover shows other band members holding instruments that I do not think are played on the album. Yet again, however, Grace’s Wikipedia entry does mention her playing recorder with her earlier band - but it also says she sometimes played the flute, as well as the oboe and clarinet.)
I play guitar in a band that features a violinist: http://thenightsky.bandcamp.com/
Cake regularly uses a trumpet. And something called a vibraslap.
The Hooters used…well, hooters or melodicas.
Hard rock band Jackyl used a Jonsered chain saw 
Introduced in “Lumberjack” but also featured in the songs “Headed for Destruction” and “Cut the Crap”
I’d say a two-stroke powered piece of power equipment qualifies as an “unusual” instrument.
Tony Levin, who was in King Crimson and Yes, plays the Stick.
Pink Floyd’s “The Gnome” features a celesta.
A number of Tilly & the Wall songs use tap dancing as the main percussion.
Kongos have an accordian solo in a hard rock setting, Apocolyptica and their cellos playing Metal covers, Pete Townsend’s use of a synth in The Who?
That reminds me: Soundgarden’s “Spoonman” had a spoon solo in it.
Do we count the vacuum cleaner solos in Phish’s live shows? (I don’t know if they used it on a studio track).
For that matter, do we count Future Man playing “drumitar” in Bela Fleck and the Flecktones?
I’m pretty sure it was used on Junta. Can’t remember what song, but I remember reading it in the liner notes.
Oh yeah, another fiddle-rock example: Yellowcard. (and Dave Mathews Band, I guess, though I don’t know if that’s just for “Ants Marching,” or all their songs)
Brian Ritchie from the Violent Femmes plays an acoustic bass a lot of the time. Not an upright bass, but what is basically bigger acoustic guitar with thicker strings.
He also plays some sort of Japanese flute and it’s a big part of his life but I don’t know what Femmes songs it appears on.
Alan Stivell tried very hard to rehabilitate the Irish harp as a rock n roll instrument.
Both Billy Joel and The Band used accordions prominently.
Taj Mahal often plays banjo, mandolin, ukulele, and kalimba. The live version of his “Ain’t Gwine Whistle Dixie (Any Mo’)” features a tuba solo by Howard Johnson (who at one point fronted an all-tuba band called Gravity)
Elton John used tap dancing (provided by the Bonzo Dog Band’s “Legs” Larry Smith) on his song “I Think I’m Gonna Kill Myself”).
Forgot to mention that the drummer just plays a snare drum with no set, and some songs feature a xylophone.
How could I forget the electric jug played by 13th Floor Elevators Svengali Tommy Hall?
The Who song “Join Together” features Jew’s harp and chord and bass harmonicas.