Jimmy Fallon and Horatio Sanz, both alumni of Saturday Night Live did this a lot.
Tim Conway and Hedley Lamar, I mean Harvey Korman, did this constantly on the Carol Burnett show.
George Burns and Jack Benny used to pal around L.A. and try to make each other crack up at inappropriate times, but I don’t know if they ever did it “professionally”. The story goes that they went to some piano recital and George said to Jack: “It would be awful if you started laughing really hard in the middle of this.” Then gave him a dead pan look and Jack couldn’t help himself.
Well, Korman would lose it not at his own lines, but at Conway’s deadpan antics. Conway himself almost never broke unless some really bizarre tangent came along, like the “siamese elephants” bit.
Korman had an excuse. It was a live show. There were a few rehersals and then the taping. Conway never did the sketchs the same in the rehersal. He would usually just practise the lines but not show what he was going to do. The great dentist sketch is a good example. Conway only told the director what was going to happen so he could get the shots. So Korman saw the sketch for the first time when the audience did and he had to try to not laugh.
To carry the hijack a little further, Carol did tell Korman about what was going to happen in her most famous scene (I saw it in a window and just couldn’t resist), simply because she feared he would not be able to keep a straight face while saying his next line.
Nobody else knew what was going to happen, and you can see the cast (and Carol) dying while trying to keep their faces straight.
Red Skelton was famous for laughing during his own routines, but you got the impression he was laughing at the audience reaction (“You’re laughing at that dumb joke?”), not his own line.
Click and Clack the Tappert Brothers are always laughing at their own and each other’s jokes on Car Talk.
On both Married With Children and Seinfeld, there were times where an actor/actress would either laugh, or act (in an out of character way) like what they just said was the cleverest line ever spoken on tv. Jerry & Al even bowed for the audience a couple times.
FWIH, Letterman affects that attitude to camouflage an extreme case of self-loathing. Miller, however, is authentically smug, which explains his popularity with neocons.
Roseanne used to do this in the first season of Roseanne, and to a lesser degree so did John Goodman and Laurie Metcalf, but on that show it worked – and I’m guessing in Goodman and Metcalf’s cases it was a conscious acting choice. They’re playing normal people, and y’know, many of us enjoy ourselves when we say something funny. I got the sense watcing those earlier seasons that part of what made this family get through the tough times was how much they got a kick out of cracking each other up, and so they took pride in coming up with punch lines. It added tremendously to the realism of the show. Far more natural than a bunch of allegedly regular people saying hilarious things with a straight face, as if they’re unaware that what they said is amusing or could be taken so.
Similarly, I didn’t mind Jerry’s amused smiles, because that’s part of the character – he’s a performer, he’s funny and a bit smug, and he likes making others laugh.
Not that every sitcom works this way – characters who are oblivious or very very dry should usually remain straightfaced – but in some cases, I don’t think it’s a problem.
And I never minded the breaks in The Carol Burnett Show or Whose Line is it Anyway; it seemed almost a challenge among the performers to screw others up, which I know is a ‘no-no’ in improv but personally I love it, it just seems so human. (Although actually in this case it’s cracking up at other people’s lines, not so much their own.)