OK, too many people in a row over the last several days have asserted the necessary inferiority of film sequels, so I'm moved to suggest a few of my favorite counterexamples:
1. The Testament of Orpheus. The mildly sfnal followup to Cocteau's second or third fantasy masterwork Orpheus, and a sort of capstone to Jean Cocteau's film career...autobiographical in the same manner as Vonnegut's Slaughterhouse-Five or any number of other fantasticated works which take advantage of the range of metaphor the fantastic allows to tell very personal truth.
2. For a Few Dollars More. An improvement over A Fistful of Dollars, less blatantly derivative of earlier films, and bettered enormously by one of the (if not the) best of Ennio Morricone's western scores. The Good, the Bad and the Ugly improves on it only to the extent that more money was available for the production of the third film, as a result of the international success of its two predecessors. (Tribute films such as The Quick and the Dead and Unforgiven ring some interesting changes.)
3-5. The Bride of Frankenstein, Dr. Phibes Rises Again, The Godfather, Part II. Three of the examples usually cited of richer, more elaborated, more engaging sequels to rather good films, at very least of their type. The original Dawn of the Dead almost makes this cut, too.
6. The Organization. While this third film about Virgil Tibbs, the second to have no relation to John Ball's novels and stories, is not a patch on In the Heat of the Night, it is a major improvement on They Call Me Mister Tibbs, and of the two sequels is closer to Ball's work, as well as an honest treatment of how relatively virtuous vigilantism frequently isn't going to triumph (and there's a nice ambiguity about how many different groups and agencies amount to the Organization of the title). Also, a cast made up of an impressive number of young actors who were going to go on to major or at least solid, briefly prominent careers, ranging from Daniel Travanti to Raul Julia to Max Gail, and good roles for underused performers such as Sheree North, Barbara McNair and Lani Miyazaki.7. Batman Returns. What can I say, I find Christopher Walken as Donald Trump, renamed as a film-geek joke for a vampire actor, a better and more interesting villain than Jack Nicholson as a too-blatantly sadistic Joker (frankly, than Heath Ledger thus, too). Michelle Pfeiffer's turn as Catwoman, almost fully-enough realized, helped, too.
8 and 9. Subspecies II: Bloodstone and Underworld: Evolution. Actually good, or good-enough, films which are sequels to terrible films, and thus both the best and worst examples here (even as, say, the second films in such franchises as Star Wars and Resident Evil, or for that matter the James Bond films, are improvements, if frequently not quite sufficient improvements). S2, however is a genuinely interesting film among a series of otherwise undistinguished work, and U:E is a less blatant example similarly.10. Before Sunset. Well, there are a number of cycles of films, of which Truffaut's Antoine Doinel series is probably the most famous (leaving aside such intentional series, not unlike television and radio series, such as The Whistler and what became of The Thin Man films...and Bond, again) that follow the life of a single character or serve as a family saga, but few if any films of that sort are so much better in their second (and probably final) installment, certainly to the degree of this one...particularly given how good, if flawed, the first is.
I'm sure there are Bergmans and similar film cycles I should be considering, but this is top of the head in the wee hours...and perhaps some special recognition should be given to nearly-as-good sequels which take a completely different tack than their predecessors (the gentle fantasy The Curse of the Cat People following the savagely satirical horror film Cat People), and works in a related medium serving as improvements on the original (one obvious example being the Buffy the Vampire Slayer television series, the film redone more in spirit it was intended...though that might more correctly be seen as more remake, as with all The Maltese Falcons and The Big Sleeps).
