Indeed, Jaws is a masterpiece, and none of the follow-ups continue the story in any worthy way. The sequels are watchable, yes, but are more like generic shark action-thrillers than follow-ups to one of the greatest movies of all time. Jaws did not need to become a franchise.
Follow-Ups: Psycho II (1983) Psycho III (1986) Psycho IV: The Beginning (1990)
Plus a remake in 1998
Psycho is a masterpiece. End of story. The story is self-contained, and everything was resolved by the end. Why oh why did they have to make a franchise out of it?! There is only one real Psycho movie.
Follow-Ups: Terminator 2: Judgment Day (1991) Terminator 3: Rise of the Machines (2003) Terminator Salvation (2009)
I know I'm in the minority here, because many regard Terminator 2 as an excellent follow-up which surpasses the original. However, as a standalone movie The Terminator works far better than it does as a franchise. Terminator 2 is good but lacks the edgy, gritty tone of the original, plus it feels more family friendly and begins to stretch the credulity of the premise. As solid as T2 is, it's not worthy of The Terminator, and I wish that the first film remained a standalone feature.
Plus you just couldn't win with a follow-up anyway. Because it seems silly for SkyNet to send a Terminator to kill an aware John Connor. Why not send it back to 1983 before the first film and kill an unwitting Sarah Connor? But if that happens, then that would mean the events of the first movie never took place because whatever happened in the past due to time travel is what always happens, what with Reese conceiving John. And the sequels get sillier because the question looms...why does SkyNet stop sending Terminators back to try and kill John? Surely there's no "three kill attempts rule". See, in the first film it was established the "time displacement equipment" was destroyed after Reese went through, yeah? Why couldn't it remain destroyed? If we establish SkyNet can manufacture one in a heartbeat (it sent a Terminator through time on many occasions after the humans had won), why does it stop trying to kill John in the past? Plus because of the principle that whatever happens in the past always happened and was destined to happen, how does it make sense for them to postpone Judgment Day? That would delay the birth of Kyle Reese and mess up the timeline, and the chances that the very same spermie will get to an egg when he fucks Sarah (he'd have to be a lot older if Judgment Day was postponed) are absolutely zero. That particular spermie would probably die off anyway. THE SEQUELS MAKE NO FUCKING SENSE!!!
Follow-Ups: The Matrix Reloaded (2003) The Matrix Revolutions (2003)
I doubt anyone can argue with this. The Matrix did not need any sequels, nor any continuation of any sort. The sequels ended up sucking (unsurprisingly), which further reflects the futility of the follow-ups. I only own the first movie on DVD & Blu-ray, and I consider the sequels as non-canon.
Follow-Ups: Poltergeist II: The Other Side (1986) Poltergeist III: The Final Chapter (1988)
Plus an upcoming remake
As a standalone movie, Poltergeist is excellent and chilling. It did not need any sequels, as they pushed things into the realm of the contrived and the incompetent. What a shame that the adorable young Heather O'Rourke died during filming of the third movie, and is thus her swansong to acting...
Follow-Ups: Highlander II: The Quickening (1991) Highlander: The Adventure Begins (1994) Highlander III: The Sorcerer (1994) Highlander: Endgame (2000) Highlander: The Source (2007) Highlander: The Search for Vengeance (2007)
Plus a few television shows...and apparently a remake is on its way.
Follow-Ups: Beneath the Planet of the Apes (1970) Escape from the Planet of the Apes (1971) Conquest of the Planet of the Apes (1972) Battle for the Planet of the Apes (1973)
Plus two TV shows, a 2001 remake, AND a 2011 prequel
I love Planet of the Apes. I love that it gets in there, tells its story, and ends on a heartbreaking note. It's a self-contained story which leaves an aura of mystery...and that's why I love it. We don't need to know everything about this world. It's because of this I've avoided the sequels and the TV show follow-ups...but I've certainly heard that they're subpar.
Follow-Ups: Halloween II (1981) Halloween III: Season of the Witch (1982) Halloween 4: The Return of Michael Myers (1988) Halloween 5 (1989) Halloween: The Curse of Michael Myers (1995) Halloween H20: 20 Years Later (1998) Halloween: Resurrection (2002)
Plus a 2007 remake, AND a sequel to said remake...
I think the lengthy list of sequels, and the brilliance of this movie really says it all...