On Friday morning (11/21), a caller to the Elliot in the Morning radio show on DC101 told the hosts that he’d recently discovered a dead body at a campsite. I was listening. I was also listening yesterday morning, when the guy called again.
This Washington Post article is supposed to be gifted – no paywall – but let me know if it doesn’t work:
Both calls are pretty memorable. 
The very great comic Peter Cook, in his declining years (and he really did decline) was, back in the '80s, a serial prank caller on LBC.
Cook occasionally called in to Clive Bull’s night-time phone-in radio show on LBC in London. Using the name “Sven from Swiss Cottage”, he mused on love, loneliness, and herrings in a mock Norwegian accent. Jokes included Sven’s attempts to find his estranged wife, in which he often claimed to be telephoning the show from all over the world, and his dislike of his fellow Norwegians’ obsession with fish. While Bull was clearly aware that Sven was fictional and was happy to play along with the joke, he did not learn of the caller’s real identity until later.
Are you wondering if there are calls preserved on YouTube? Of course there are. Here’s an example.
Damn. The quote came from his wiki page (see the last para of the section on the 1980s). Too much bother to edit the previous post - links to YouTube and all that.
j
In Telluride CO there is one public radio station (that is great!): KOTO. Being public, they do quarterly fund drives. Back in the nineties on a construction site, this station was pretty much the only source of music unless you wanted to deal with cassettes or CDs. One fund drive the hosts were being truly obnoxious–playing 30 seconds of a song, then cutting it off to beg for money, over and over. One of my coworkers called in: (On air) “KOTO, would you like to donate?” “SHUT. THE. FUCK. UP!!!”, click. Radio silence, then “Well, an editorial comment from a listener…”
Car Talk had some memorable callers over the years as well. The one I will always remember was the woman who called in to relate the story of how she accidentally got in a coins only lane at a toll booth, and because she didn’t actually have the $2 in coins or whatever, so she just blew through the toll without paying. And then their producer actually managed to get the manager from the toll agency where this happened on the phone!
Car Talk also once got a call from the International Space Station.
On a completely different note, when I was in high school, there was a caller on the morning drive time show on the local alternative rock station in Charlotte, ostensibly to complain about the vulgarity of one of the show or something like that. Then he gave his name – Mike Hunt (Say it out loud, “Mike Hunt” sounds like something vulgar itself). I’m 99.9% sure that call was either staged by the radio station, or a prank. Probably the former. But people at school that morning were talking about is as if a real guy named Mike Hunt had called into the show.
I think this is the one. It’s famous among broadcasters.
(Sorry deleted again.. having weird format issues?)
Garrison Keillor did a version of that sketch on A Prairie Home Companion:
GARRISON: Radio is a powerful medium, it’s more real than television ---- on television, you can sit and watch cars blow up, guys be mowed down by machine gun fire, and eat your dinner through the whole thing, but with radio ---- sometimes we’ve presented simple, non- life-threatening medical procedures on the show and people almost toss their cookies…(RESPIRATOR, CLINK OF INSTRUMENTS)…
DOCTOR: Okay, we’re all set, Mr. Briggs…we’re only using a local anesthetic because we need you to be able to hold your eye open while we snip off the retina, okay? You all set, Mr. Briggs? Just raise your index finger any time you want me to stop, okay? Good. Nice and relaxed now. Hold your head steady. That’s right. Just look straight at the scissors, Mr. Briggs. Straight at the scissors. (SNIP) There. Very good. Now the left eye…
There was a Radiolab episode that elicited a similar effect, where they were talking about a woman having open heart surgery. They gave a warning but man, I was not prepared for that.