Many animators were also puppet makers, at least to begin with. Later in their career they may have had others to take on some of the stages of puppet making. First ones to come to mind, who are no longer with us, are:
Ladislas Starewitch, Ray Harryhausen, and David Allen.
And of course in a lot of newer/bigger productions the job might be tasked out to many people - one might design armatures, another or maybe several to build them, then a team of rubber casters and fabricators, plus other teams for details like hair, clothing etc. That said, and to get back to the classic (semi I suppose) creature puppet stuff - Phil Tippett was known to crank out some nice puppets. The Quays build their own, albeit from spare parts and antique scraps. Eva Svankmajer made some really sweet puppets for her husband's films (I think - not sure how much of the puppet construction she handled - possibly mainly design).
Nick Hilligoss, Ron Cole, Lionel Ivan Orozco, Marc Spess...
(Those are people from this forum - not what you'd call famous puppet builders, but pretty durn famous round these here parts anyway!)
Oh oops! I missed that they're supposed to be passed on.. all the ones I mentioned are still alive and kickin'. But one day this post will be relevant!
Sheesh Strider, I had to check my pulse... Nope, not kicked the bucket yet.
Stan Winston definitely made live action/cable/animatronic puppets, not sure if he ever made any stopmotion puppets.
Arthur Hayward is probably dead, but haven't found out for sure. Some of his museum diorama work is here: https://www.youtube.com/watch?v=YO5xzo44J7I
Thought of another one. Stephen Czerkas made and animated stop motion dinosaurs for Planet of Dinosaurs (1977) and a number of other projects, eventually becoming a noted palaeoartist and opening his own dinosaur museum in Utah.
As it happens, today is the first anniversary of his death, on 22 January 2015. http://dinosaur-museum.org/stephenczerkasmemorial.htm
I googled Arthur Hayward but got hits for an artist, a cricketer, and a few other people, couldn't find a bio.
Another one - Wah Chang. Born 1917, died 2003. https://en.wikipedia.org/wiki/Wah_Chang
According to Ray's Century of Model Animation, he sculpted and constructed the dragon for Wonderful World of the Brothers Grimm (1962). He also made some puppets for 7 Faces of Dr Lao I think, and the puppets for Jack the Giant Killer, among others in a long career.