Will Smith's character name in the show is actually different than in real life. In the show, he is "William" Smith, in real life he's "Willard" Smith. This is referred to when one of Will's girlfriend's father calls him Williard as a joke.
The part of Aunt Vivian Banks was portrayed by two different actresses during the series run. 'Janet Hubert-Whitten' portrayed the original Vivian during seasons 1-3, but growing problems between Will Smith, the producers, and Hubert-Whitten caused her to depart in 1994. The producers offered Hubert-Whitten a 12/25 contract for season four, but she declined. Daphne Maxwell Reid replaced her in the role from 1994-1996, seasons 4-6.
The running gag of the "Carlton Dance" throughout the show was actually a parody of the dance Courteney Cox did on the Bruce Springsteen music video "Dancing in the Dark" in 1984.
The show was originally canceled by NBC after the fourth season, with the series finale being the episode where Will moves back to Philadelphia. However, fan reaction and letters written to Will Smith and NBC persuaded them to renew the show and it ended up continuing for two more seasons.
May have been the first TV series saved from cancellation by pleas from TV-station managers. The show aired its 1990-1994 episodes in syndication after the fourth season while running the fifth season on network. At the end of that season, NBC wanted to pull the plug because the new episodes were getting a mediocre 8.6 rating. But the reruns were drawing a 7.4, extremely good for an ad-hoc collection of shows you've seen three or four times, and the managers of the local stations thought they might have one of those "phenom" series where people religiously watch their favorite episodes and a lot of them. To avoid over-running the shows they already had (about a hundred, already run three times), the station managers agreed to buy the fifth and sixth seasons at a greatly inflated price (adding 50 more shows to their libraries and helping avoid burning out the audiences) - meaning NBC would NOT lose money by picking up the show after all.
Sherman Hemsley appeared as two different characters throughout the show, once as Judge Carl Robertson and again later as a cameo playing George Jefferson
Nicky's full name is Nicholas Michael Shawn Nathan Wanya Banks. He is named after the four members of Boyz II Men, after they performed at his christening.
As it required on-location shooting, only one shot of Jazz being thrown out of the house was done (with only a few exceptions). Therefore, to avoid continuity errors, it is made sure that Jazz is always wearing the same shirt in episodes where he's thrown out.
According to Will Smith in an interview, the reason for his character being named "Will Smith" was that, during the creation of the show, he and Alfonso Ribeiro were brainstorming names for their characters. Alfonso remarked that Will had to be careful in naming his character, as people would refer to him in public by that name for the rest of his life, and suggested that he name the character "Will Smith".