Howard Stern lives this trope on the show. While he savages other celebrities, rival radio hosts and his own crew, he also spends a lot of time making fun of his small penis (though later he found out he's actually fairly normal, he's just reall tall and it looks small on him), his big nose, his nuerosis, etc.
I'm Sorry I Haven't A Clue lived and breathed this trope, with the late Chairman Humph being baffled that anyone was listening to this rubbish. Chairman Jack continues this tradition.
This was a direct continuation of I'm Sorry, I'll Read That Again, in which not just the late Announcer Hatch, but the cast was baffled that anyone was listening to this rubbish. Later episodes also made fun of the performers' careers outside Radio Prune, leading to the pleasing symmetry of Clue's parent show slagging it off after the first season:
Director-General of the BBC: I'm Sorry I Haven't A Script, that was you lot, wasn't it? Call that a Panel Game? Don't make me laugh. Bill Oddie: We didn't.
The competitors also engaged in it themselves, on occassion — in the "Broadcasting Ball" episode, the contestants were to identify a sound or bit of music. A quick, monkeyesque 'ooo ooo ooo' played for Tim, to which he responded with this.
Tim: Well, that'd be three geriatrics called The Goodies attempting to sing.
(the clip is played again, slightly longer this time, with audience cheers in the background)
Tim: Hold on, that can't be The Goodies, that's applause...
Most comedy shows on American public radio generally make fun of public radio, as being too liberal, too erudite, too boring, or what have you.
Tom or Ray Magliozzi: Well, it's happened again - you've wasted another perfectly good hour listening to Car Talk... and even though Roger Clemens stabs his radio with a syringe whenever he hears us say it, this is NPR: National Public Radio.
Garrison Keillor on A Prairie Home Companion relies on self-deprecating humor all the time, most famously by discussing the foibles of rural Minnesotans, but also referring to himself as having "a face made for radio", referring to the show as "this job I picked up on the weekends", and so forth.
Much of Ricky Gervais and Steve Merchant's radio show consisted of them expressing amazement at how bad the show was and apologizing to the listeners (or suggesting that there no longer were any). They usually blamed Karl, particularly if he was in charge of a feature like Rockbusters or Monkey News, but also for the long stretches of silence that would sometimes follow if he was asked a question. They also got a kick out of reading the abusive emails they got from hostile listener Richard Anderson ("Dickers!")
The late Radio 1 DJ John Peel frequently poked fun at himself on his radio show, from his looks to the way he would sometimes play records at the wrong speed (back when DJs spun vinyl records) to how much time he spent listening to demo tapes from young upstart bands clamoring for a chance to be on his show.
Hamish And Andy: When Hamish got fat many jokes were made about it. Hamish made more jokes about it then Andy
On The Tony Kornheiser Show, many self deprecating jokes are made about the show's quality. The show's email address, This Show Stinks, bears that out.
LA morning show hosts Kevin and Bean on KROQ get a lot of mileage out of criticizing the production value of their show, the skills of their co-workers, and their own idiosyncrasies. This was one of the big tonal differences between them and their long-time rivals, Mark and Brian on KLOS, who spared few opportunities to express pride in their show and comic timing.
The radio show Hello Cheeky starred performers Tim Brooke-Taylor, Barry Cryer and John Junkin, who also wrote the scripts. Thus, the leads wrote jokes against themselves. It's frequently mentioned that the show only has one listener ("Hello, Eric"), and episodes with guest stars generally focus on the guest star trying to comprehend the rubbish they get away with.
John:(reading a letter) Dear John Junkin — quit comedy and stick to straight acting. Yours, Tim Brooke-Taylor and Barry Cryer?! Here, fellas, I want a word with you!
Also, in later seasons, a section of the show was reserved for the fictional post they received. No insults were spared.
Dear Hello Cheeky, I was wondering if you could help me. On second thoughts, if I'm writing to you, I must be beyond help.