Rent "Scream 3" for some movie lover's insights into trilogies.
My own opinions:
LOTR was conceived as a film interpretation of a book series. It didn't start as a single movie then branch into a trilogy; its very conception was to be a huge story divided into three more manageable sections. All three were brilliant, though I would pick part two as my favorite (for the battle scenes and the action with Gollum and the hobbits).
Star Wars is a little hard to nail down because it started as a single movie that blossomed into a six-movie franchise (plus about four TV and cable movies related to the SW universe, plus a chain of novels and comics). Lucas had a specific story in mind, but it wasn't put into canonized book form prior to the first film's release. Therefore, it's hard to say for sure what his vision was intended to be from the beginning. As for each film's merits (considering the first three to be "the trilogy"
, I rate them thus: 1) Star Wars, 2) Return of the Jedi and 3) The Empire Strikes Back (only because of the downer ending and the absence of a big, climactic space battle).
Die Hard: a great idea (for the 80's) about a makes-his-own-rules cop caught up in a situation where his heroism shines (and allows the studios to do some impressive shooting/explosion sequences). The second movie, while it had its merits, was mostly awful, if for no other reason than it was FAR too coincidental that such a similar thing happened to the same cop. The third movie was more realistic in that respect, though it suffered by requiring Sam Jackson's character as a film-length "sidekick" where none was really needed.
The "Alien" series, while technically not a trilogy, suffered the same fate as many other movie franchises; the first movie was original and entertaining, the second took the same characters (Ripley and the aliens) and created a new story around them, while the third and fourth simply re-hashed part two.
"The Godfather" part III was one of the biggest mistakes in cinema history. I would rather have seen a VH1 reunion special; at least that wouldn't have featured Sophia Coppola. The first two movies are legendary, of course, but the third just puts a big dose of Alzheimer's on it.