This is a great topic, and the list is indeed quite small.

The Godfather Part II is considered by many to be better than the first one, and though the first one comes out ahead at IMDB, I'd put 'em about even. Part III is universally hated, although I still think it's a good film.

A lot of peopole think The Last Crusade was better than Raiders of The Lost Ark, I tend to disagree there, but that one comes pretty close to the original. Temple of Doom was kind of a letdown.

I personally liked Lethal Weapon 2 and even 3 better than the first, but I can see why most people disagree there.

I think that Rocky II comes really close, and if it weren't for the third, fourth, fifth, and seventy-third volumes, conventional wisdom might agree with me.

Along the comic book lines, Superman 2 was definitely better than the first.

Then there's Evil Dead II...