RE: Saw IV
Star Trek II: The Wrath of Khan Star Wars: The Empire Strikes Back Spider-Man 2
Those are a few sequels widely regarded as superior to the original.
I saw the first Saw on video well after it came out; thought it a good premise executed so-so. Haven't bothered to see the sequels, though maybe I should based on Joe's recommendation.
But Kate's right -- generally speaking, sequels usually suck. Ghostbusters II. Another 48 Hours. Pirates of the Caribbean: Dead Man's Chest. Ocean's Twelve. These are movies so bad, they dim your appreciation of the first one, too.
Biggest fall from grace for me was a tie between Spider-Man 3 and Shrek 3. From fresh and fun to utterly craptastic.

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