"Prematurely", of course, is in the mind of the beholder. There are lists of shows that got cancelled; not looking for that. The question here is what shows would you wish had gone on longer.
Three regrettably-axed series come to mind for me:
Deadwood
Firefly
Freaks and Geeks
Another one I would add is "Star Trek: Enterprise" [part of the Star Trek franchise, and also referred to as just "Enterprise"] which I thought was good but it ended after just four series which was well short of the sevenness one might have expected of a Star Trek series. I believe it was cancelled.
Star Trek: the original series ~ 1968 - 1969
The now famous TV show was cancelled after Series 3. Punitive (and it is alleged by cast and fans, deliberate) budget cuts in the final series undermined quality, impacted ratings, and the show was cancelled. It seems ludicrous today that a widely loved and admired TV series which grew in one of the biggest global TV and movie franchises of all time, could be hamstrung and killed off by NBC in 1969 a few months before the Apollo 11 moon shot.
Star Trek was nearly cancelled before episode 1 as the production company Desilu (owned and led by TV icon Lucile Ball) was in dept and already struggling with Mission Impossible.
Mid season 1 after suffering from a mixed audience response, which at the time included a then unrecognised and relatively small cult/core following, the show was seen by broadcaster NBC as being too cerebral and was under pressure. The then relatively small but significant cult following wrote hundreds of thousands of letters, saving the show in series 2, but were unable to overcome the budget cut induced decline in series 3.
However Series 3 took the episode count up to nearly 80 enabling the show to be syndicated and re-run and re-rerun for the next few years when it built a wider audience and appeal as viewers came to appreciate the nuances of the characters, the societal topics address and the pseudo-religious and anti-authoritarian angles pitched in many episodes.
A decade after being cancelled Star Trek: the original series had earned Paramount, who by then owned the syndicated rights, a million dollars per episode. In 2011, the decision to cancel Star Trek by NBC was ranked 4th in the TV Guide Network special, “25 Biggest TV Blunders”. After the success of Star Wars in 1977, Paramount commissioned and produced Star Trek: the Motion Picture which was released in 1979. By 1999 the expanded franchise had grossed around 8 billion dollars and is one of the highest grossing media franchises of all time.
