Hank Williams/Hank Williams Jr./Hank Williams III all became famous in their own right.
Conrad Hilton/his sons Barron & Nicky Hilton/the current Hiltons are all better known than most hotel families would be (i.e. none of the Marriotts or Statlers are famous or infamous)
I would totally watch Joss Whedon’s Sesame Street.
A little more obscure, but the Udall family is doing pretty well for itself, including two current U.S. senators: Udall family - Wikipedia
The Barrymore familygoes back at least a century and a half, especially if you’re counting the Drew branch, which is a notable acting family in its own right. Acting families like that are fairly common; consider the Kembles, a famous British acting family, and the Booths, a rather infamous American one.
Woody Guthrie/Arlo Guthrie/Sarah Lee Guthrie
'Cause nobody doesn’t like Sarah Lee.
Crispin Mills, singer, son of Hayley Mills, nephew of Juliet Mills and grandson of Sir John Mlls.
And Emma Freud.
Another one with a skipped generation is Tyrone Power, Tyrone Power, and Tyrone Power. Tyrone Power, Jr. was in a few movies, as well.
In classical music, there were quite a few Bachs and Strausses, but I’m not sure how many actual generations were involved.
5 generations of famous Rockefellers:
John D. Rockefeller, Sr.
John D. Rockefeller, Jr.
John D. Rockefeller III
Sen. Jay Rockefeller
Justin Rockefeller
And many of their siblings have also been famous.
James Packer, Australian businessman. Son of Kerry Packer, and grandson of Sir Frank Packer.
And one of the Booths descendants is Cherie Blair/Booth wife of former Prime Minister Tony via her actor father, also Tony.
In the history of astronomy there are the four generations of the Cassini family who were successively the first four directors of the Paris Observatory. To avoid confusion, the convention has had to be established of referring to them as Cassini I, II, III and IV.
But this, like several examples in the thread, is really just an example of a “family firm”. Only Cassini I was truly exceptional and independently famous, with the others then good enough to inherit the position from their father.
Peter Benchley was the son of Nathaniel Benchley and grandson of Robert Benchley (of Algonquin Round Table fame).
Huh. I always wondered how all the Benchleys fit together. Ignorance fought - thanks!
Bret Boone played with David Bell, who was the son of Buddy Bell, who was the son of Gus Bell. Two third generation MLB players who played together.
Carmine Coppola
Francis Coppola
Sophia Coppola
Clifford Arquette (Charlie Weaver), his son Lewis Arquette, and all the Arquette grandchildren: Patricia, Rosanna, Alexis (formerly Robert), Richmond and David.
In my own neck of the woods, Dwight Morrow was a famous stateman and ambassador to Mexico, his daughter Anne married Charles Lindberg and wrote really good books, and their daughter Anne Lindberg writes children’s books.
John Farrow & Maureen O’Sullivan had Mia, whose adopted daughter Soon-Yi is well known.
Thalia Shire and Nicholas Cage are also a part of the family. Some good show biz genes there.
More racing.
The Andrettis: Mario and his brother Marco, Mario’s son Michael, and Michael’s son Marco.
The Unsers: Al Sr. (Big Al) begat Al Jr. (Little Al) begat Al III (Mini Al).