Okay you got me. Interestingly enough 3 out of 4 of the movies that had great sequels were in the 1980s.
Some of the best movies were made in the 80's. It's a solid decade, probably my favourite decade of film, just beating out the 90's. Some other great sequels: LOTR: The Two Towers and LOTR: The Return of the King Spider-Man 2 (2004) Star Trek II: The Wrath of Khan (some might argue that the first film wasn't very good, so it wouldn't meet your original criteria) The Godfather Part II Indiana Jones and the Last Crusade (my personal favourite of the series)
I didn't mean those two example were the only ones, just the only ones that came to my mind at that time. That said, The Two Towers does not fit my criteria because all three movies were filmed in one go much like Back to the Future. Unrelated note, The Two Towers was easily my favorite book of the series. By my criteria, a sequel has to not have been guaranteed. I never saw the Godfather series, I should, I only hear good things about it but I never got around to it. I remember an old web comic "So why are the odd and even numbered Star Trek movies on different shelves?" "That's intentional." "Where's Star Trek 5?" "That's on the Wall of Shame." Spiderman 2 would qualify I guess by popular opinion. A lot of people say it is the best of the Sam Raimi trilogy but I personally like 1 and 2 equally.
Sequels better (or good as) the original? Not included in a programmed trilogy / whatever? Still not mentioned: SHREK 2
I loved the original Shrek. Shrek 2 was good, but IMHO was not as good as or better than the original.
I specifically mentioned non-animated movies. I think Shrek 2, Kung Fu Panda 2, last night I had more but now I'm drawing a blank.