Just some thoughts
Most of these have been mentioned, but here's my 2 cents. These comments are my opinions, not just following the thread observations. I'm talking horror/sci-fi, so I'm skipping the Godfather debates. And I think you can make an argument Last Crusade is better than Raiders, but I'm pretty sure I'm in the minority there.
Aliens - the best horror/sci-fi sequel ever, IMHO.
Phantasm II - better movie, not just better looking.
NOES 3: Dream Warriors - I think it's the best of the series.
F13 4: Final Chapter - again, I think it's the best of the series.
Star Trek II - I'm not a Trekkie, but I like this one.
You can easily make an argument for T2 and Evil Dead 2, but both originals to me have a sort of "raw" feel that can't be made up for by the better production values, as opposed to Phantasm II, which I think is a better movie as well as having better production values.
I disagree on the Empire/Star Wars superiority, though I enjoy both movies (and Return of the Jedi).
Silence of the Lambs is better than Manhunter, but I don't consider it a true sequel.
And it's not that I don't like NOES or the original F13, I just think some of their sequels top them - we're talking good vs. very good, not just bad vs. good.
And I think Jaws 2 and Halloween 2 are both pretty good movies, but both pale in comparison to the originals, diminishing their reputations.