One of the things that I loved (that I would later see on Saturday Night Live skits) is when the comedians would be cracking themselves up in the middle of the skit and trying to hold back the laughter while playing their roles.
I think it was Saturday Night Live in the late 1970's that finally took over where the Carol Burnett show left off. Saturday Night live started in 1975, but it didn't really catch on in the popular culture until around 1978-1979. I think part of what made the show for a younger audience was rock bands playing live music on the show. I recall first seeing Jackson Browne singing "Runnning On Empty", and David Byrne/Talking Heads singing "Take me to the River". Many of these I was hearing for the first time, and not on the radio.
I was watching Saturday Night Live after Steve Martin left the show to be a standup comic, and I already had several of his albumes before I knew he used to be on SNL. Belushi, Bill Murray, Jane Curtin, Garret Morris, Gilda Radner, Dan Akroid. Glory days...