Obvious and already stated but:
Godfather Part 2
Empire Strikes Back
Spiderman 2
Dark Knight
Wrath of Khan
Also OP technically Two Towers isn't a sequel. There's only one film/novel called Lord of the Rings that was chopped into three to make it more consumable to joe public size wise so all you're really saying is you liked the middle of the film more. Pedantic I know but it always annoys me when people don't factor this element of LOTR in when they talk about sequels, planning out story etc.
Love the Temple of Doom mention too. Completely wrong but nice to see preaching for the underdog!
Actually, there's one novel called The Lord of the Rings, but for publishing reasons it got cut up in three volumes; The Fellowship of the Ring, The Two Towers and The Return of the King. The sheer amount of story told in the three volumes could not contained in one single film, so splitting the story up in three movies that roughly follows the same cutting lines the novel had (some content was shifted IIRC) was a correct call. The entire trilogy doesn't have too much filler content.
I think you are confused with The Hobbit, which was originally intended as a two-part movie (An Unexpected Journey and There And Back Again), but WB in all it's infinite wisdom decided to make it a three-parter like LOTR. Considering the Hobbit novel didn't have as much content as LOTR had, Jackson & Co had to make a lot of stuff up and stuff it with nonsensical filler content.
OT:
the sequels that are better than their predecessors IMHO:
Godfather 2
Terminator 2
Aliens
Clerks 2
Batman Returns
The Dark Knight
Toy Story 2
Toy Story 3
Lethal Weapon 2
Mad Max: Beyond Thunderdome
X-Men 2
Spider-Man 2
Empire Strikes Back