Over the years, I’ve heard a number of interviews with Joe Walsh, primarily on Steve Dahl’s radio show here in Chicago. He was always very funny, and very self-effacing.
Bill Bailey.
Thirty-odd years ago I saw Leon Redbone a couple of times as support for Leo Kottke. His stage banter was very funny and he would throw in dramatic embellishments to his strumming that raised a chuckle.
Unexpectedly funny: June Carter. She was playing with Johnny Cash during one of his last tours when he wasn’t well at all. Johnny played for a few songs and then had to step backstage. Turned out he never came back out but June carried on like a fucking rock star and was entertaining as hell. Walked out of that show with mixed emotions for sure, but happy with what I saw.
(paraphrasing)
Reporter: How many protest singers like you are there?
A media-weary Bob Dylan: 136. Or maybe 143. I think it’s 136 or 143.
mmm
Josh Groban’s music is banal but he is ludicrously funny. His musical rendition of Kanye West tweets is amusing but if you can find a full video of the time he hosted (not appeared on but actually hosted) British music-themed comedy panel show “Never Mind the Buzzcocks” I heartily recommend a watch.
(US viewers will need to know that “HRT” stands for “hormone replacement therapy”, used by postmenopausal women, to get one of the better gags.)
Seconding this. I’ve seen him a number of times in concert and his stage banter is often hilarious. It’s sometimes like watching a comedian handling hecklers, since the audiences can be quite vocal at times.
And there’s the whole “1000 Years of Popular Music” thing (of which, I believe, “Ooops I Did It Again” is part of). Back in 1999 Playboy asked a number of musicians and music industry insiders to submit lists of what they thought were the top 10 songs of the millenium. Figuring most people’s lists would start somewhere in the 1950s, Thompson decided to take them literally and compiled a list of popular music stretching all the way back to the 11th century. 
Was just listening to John Prine’s old Dear Abby on the car stereo yesterday. He has the ability to be both serious and funny.
Signed,
Noisemaker.
Remember – the Beatles got their recording contract because of their sense of humor.
I think most groups, even serious ones, sit down and start doing something silly from time to time. Cream did “Mother’s Lament,” Procol Harum did “Mabel,” and the Who did several. John Entwistle in particular wrote songs that were darkly humorous.
Bo Burnham. My favorite song of his is “Oh Bo”, which is hilarious but very NSFW on the lyrics.
Another favorite is Don McCloskey. The video of this one doesn’t appear to be on YouTube anymore, but the song still is: “King of Discount Ho’s”. Also NSFW lyrics.
I can’t personally vouch for them, but I did find this list of The funniest classical musicians, past and present. (#1 on the list is Victor Borge, but I don’t think any of the others have been mentioned yet, and many of them I hadn’t heard of.)
The Goons - Unchained Melody
I'm walking backwards for Christmas
Forgot one: The Doubleclicks. Exhibit A: “The Guy Who Yelled Free Bird”.
Spikes Jones & His City Slickers - well capable of playing straight but most of the time they took songs that were widely covered and did them again, in their own way.
William Tell Overture Spike Jones William Tell Overture - YouTube
That Old Black Magic - YouTube
They especially used to take cloying sentimental old sloppy standards and demolish them
Tennessee Waltz Spike Jones And His City Slickers - Tennessee Waltz - YouTube
Cocktales for two SPIKE JONES & CITY SLICKERS - COCKTAILS FOR TWO - 1945 - YouTube
Tom Lehrer
Poisoning Pigeons in the park
The Masochism Tango
We’re including deceased musicians? I nominate Mozart, who wrote A Musical Joke. Doesn’t seem as funny now; I guess you had to be there. Have you laughed at parallel fifths recently?
Anna Russell. I saw her once in concert, but she wouldn’t be on my hot list.
Mark Russel could deliver some good laughs.
Definitely funny in In Spite of Ourselves, and his story before the song.
June was always the “funny one” from the Carter Sisters, she developed that persona to cover up for her (in her opinion) lack of singing ability. That would be back in the 50s when they were doing regular radio shows.
I was fortunate enough to see Johnny Cash at his last UK show, and he was usually on stage for 4 or 5 songs at a time, whilst his band and family performed in between. June was definitely funny then, and in my opinion sounded better singing than she did when she was younger.
Cash himself had a pretty dry, self-effacing sense of humour when he cared to show it, but that side of him has been covered up a bit by the “Man In Black” persona.
IRRC, That went more like, “My grandfather gave me this watch…a few minutes before he died…for twenty bucks…plus tax.”
You might find it interesting to know that Prof. Schickele has performed intimate, one and two-man concerts in small venues, prefacing them with the claim that “none” of the material had anything to do with PDQ (so if that’s what you came for, please leave now!). I happened to attend one such concert some years ago, where he performed all original material that he said he wrote to pass the time while on the road, mostly clever or humorous ditties. I hope that he will record some of these before they are lost to the ages, as they are worth preserving.
All I can remember of detail is one song he wrote after passing thru the New England countryside near New Bethel, NY, the former site of the Woodstock Festival. Seeing cows in the field, he said, “Here we are at Woodstock. Would stock appreciate it if they could?..”