By no means exhaustive, but there are some I had not come across here.
It's about a half a minute long, but THE SIMPSON nails this promo for "Star Trek XII: So Very Tired" so very well.
From THE MAVIS BRAMSTON SHOW, a 1960s Australian comedy series. This is new to me and the only clip from a show parodying STAR TREK during its initial network run!
"Star Schtick" from an early 1970s WAYNE & SCHUSTER CBC comedy show. This is mini-epic in length, standard schtick (natch!) in cleverness.
Carol Burnett (with the wonderful Andrea Martin) from a 1991 one-shot (and probable pilot for a new Burnett variety show) titled, uh, THE CAROL BURNETT SHOW according to IMDB. More than likely, it may be from a short lived series titled CAROL & COMPANY:
THE WONDER YEARS parodies the "Spock's Brain" episode.
The one and only Kevin Pollak from a stand up routine in the months before the release of STAR TREK V. Pollak is the gold standard of Shatner impersonators.
"Star Truck" from the ANIMANIACS show:
"Steam Trek:" STAR TREK THE MOTION PICTURE as a silent movie, complete with tinkly piano music. This has been on YouTube for a couple of years.
Jim Carrey as Kirk in "The Wrath of Farrakhan" spoof from the Fox TV series IN LIVING COLOR.
The best: Belushi as Kirk for SNL, written by Trekker Michael O'Donoghue.