College basketball coaches. Well, one anyway.
For me it’s the lager phone, nothing says inbred more than this.
Well, for it has to be the accordion. Not sure why. They were quite common prior to Rock N Roll. Somehow they got to be the butt of jokes.
We used to throw crumpled up paper into the Tubas in band hall. The paper would go flying out when the band practiced. 
A mouth Harp is annoying. That twang, twang sound. I haven’t seen anybody play one in decades. You wouldn’t get much respect if you did.
And he never knows when to come in.
First thing I thought of was the sad trombone.
Tuba players are such divas!
;^)
The stereotype about viola players not being as good as violin players has a small basis in fact: There are WAAAAAAYYY more violin players than viola players, so there is less competition for seats in the orchestra. You have to be REALLY good to get a spot in a good orchestra playing violin; You only have to be good to get a spot playing viola.
A merely good violin player might get tired of playing, literally, second fiddle, and trade in the violin to secure a first-chair viola position. At the cost of being the butt of all the viola jokes.
What has seven arms and sucks?
Def Lepard.
You know, the accordion almost wasn’t the butt of all jokes.
I once saw a performance by Peter Schickele (as opposed to the character P.D.Q. Bach) and while he did all the musical instrument/musician jokes, he seemed to spend the most time skewering the viola.
Accordions are common in Newfoundland music. Great Big Sea has done some pop music with accordions.
A few rock groups have done guitar/bagpipe combos, the aforementioned Great Big Sea is one, another is Off Kilter.
My jazz musician brother tells these:
Q: Define an optimist
A: A trombone player who carries a beeper
Q: What’s the difference between a frog walking down the street and a trombone player walking down the street?
A: The frog might be going to a gig
I play guitar, Dobro and lap steel guitar. Most who play the first make fun of the other two. Some people call the Dobro the ‘Hillbilly Trombone.’
This morning, police received a report of a group of men in the park wearing dresses and torturing cats. Further investigation revealed that they were just bagpipers.
The accordionist from Golden Bough told this story:
The problem with an accordion is its size. I was on the way to a gig and stopped by a 7/11 for a quick snack. Of course, I had to leave the accordion in the car, and I must have forgotten to lock the door. I was only inside for five minutes, but when I got back … two accordions!
Has anyone mentioned the sackbut?
Surely, Le Pétomane and his musical instrument must be the butt of innumerable jokes, or so one would expect.
ETA: And yes, sackbut was mentioned earlier up-thread.
Bass guitar - least skilled and least important band member. Even groupies avoid him. It’s basically seen as Easy Mode Guitar. Drums get similar flack, but not as bad, and every band needs percussion. Not every band needs a bass.
Tuba - played by fat people
Saxophone has a “sexy” vibe, but often associated with cheesy Kenny G. I don’t get the first part, it is an objectively awful instrument.
Yes, accordion is specifically nerdy. It doesn’t help that They Might Be Giants was the go-to 1990s geek band. Also ethnic street musician vibe, although that is sometime a concertina.
As a non-band person, I think most people aren’t aware that the viola is a different instrument than a violin. I’m not sure I could tell them apart unless they were side-by-side. The only viola player I know is John Cale.
Obligatory cello link. Either the players can’t play anything else but need the band credit, or serious cello players are geeks. Clarinet is the generic school band instrument, nothing bad about it just boring. And I don’t know any jokes, but I’m sure there’s something about being 8th clarinet.
Accordions and bagpipes are awesome and I will fight anyone over it. Triangle is cool since SNL.
“The difference between a violin and a viola is that a viola will burn longer.”
- Victor Borge
Piccolo stereotypes are generally that they’re never in tune.
In fairness, as a piccolo player they really are notoriously difficult to tune, and as wind instruments they tend to drift out of tune as they warm up. Since they’re really small, IME they tend to drift more direly than larger instruments.
I’d say that when I was in band, drummers were generally the butt of the most jokes.
Clarinets were next, despite being probably the most numerous instrument in the band. The stereotype was essentially that if Zooey Deschanel had to play a band geek in a movie, the role would be a clarinet player. That wasn’t the explicit joke, but that’s the idea of how they were viewed, kind of a quirky, weird Hollywood-safe hipster type.
Flute players are pretty or whatever.
Trumpets are loud and egotistical. Saxophones were trumpet players with better hair.
Oboes got to share the Piccolo tuning jokes.
The rest of the instruments didn’t really have any unique jokes that stuck. Generally larger instruments had a “dumb” stereotype of some sort. French horns had some weird joke attached to them that everything they did was to please the Horn Gods, but it wasn’t consistent.
These were the general stereotypes that seemed to be common no matter who you were talking to. Individual bands had their own stereotypes. In our band Trombones were known for being a bit hyper and kind of nerdy, and that’s largely because we were, in fact, that.