All In The Family was the most impactful. It so commanded the airwaves in its time that other shows were launched around it. Even Nixon was said to avoid airing presidential addresses during the show. It gave us Maude, The Jeffersons, "Meathead", "Dingbat", and something to talk about at school on Monday. It was loosely based on Britain's "Till Death Do Us Part" which aired several years earlier...but Family had much more force in ratings. At the time, Archie was regularly voted as most popular television character, while Edith was voted as most lovable. It spent more time at number one in the Nielsens than any other show, until American Idol.
The Honeymooners was a spin-off of The Jackie Gleason Show...kind of like The Simpsons was an animated skit from Tracy Ullman's show. It only lasted one season, but was preceded by extensive live stage presentations that were not aired. Audrey Meadows was almost booted as Ralph's wife, until she convinced Gleason that she could make herself look less pretty.
I Love Lucy went six seasons. A fun story about the show, is that Vivian Vance and William Frawley hated each other...to the point that they had it put into their contracts that they each spent a limited amount of time in front of the camera together. Desilu was the production company. They ended up buying the rights to The Twilight Zone and Star Trek after they went into syndication.