+1
Star Wars
I'd say Star Wars. Each of the movies are solid quality fliks and both sequels are meaningful follow-ups to the movie before.
The Lord of the Rings
The problem with LOTR is that it goes overlong, especially if you watch the extended cut. So much of the over-arching dilemma of destroying the One Ring gets lost among sidequests like defeating Shelob, Saruman, this siege or that. Were it representative of the content of a video game, I'd have no complaints, but as a series of movies stringing together a coherent plot, there's way too many flashbacks to Rivendell.
The Dark Knight
The Dark Knight was unquestionably the best of the three movies, and while I'd also contend that the second movie in Star Wars is my favorite, the consistency in DK is all over the place. Batman Begins starts off way too slow, not even Liam Neeson can make me remember his characters' name (Raws-Al-Ghoul?) and the whole training to become a ninja thing always felt goofy. The Scarecrow isn't a bad villain, but he fills way too little space in the movie, unlike Joker. On the flipside, Bane is in way too much of Dark Knight Rises, he doesn't resemble his comicbook counterpart at all and feels like a ludicrously over-inflated sideshow in contrast to Joker. The movie just overall was... crummy. Easily the worst I've seen of Nolan's, and after you've already whipped out your arch-enemy in the second movie and layered it over with so much symbolism, a plothole-ridden sub-par adaptation of the villain-of-the-week just doesn't cut it.
Considering how the first movie gives us our origin story, the second movie sets up the third by portraying Batman as the public enemy of Gotham, a truly effective third movie could have been one in which, instead of crippling Batman in a hole for the majority of the movie so you can cram in some stupid "Rise" gimmick, actually have him face-off against an ensemble of classic enemies he's accrued over the years as he struggles not to break his one rule and actually become the enemy of Gotham he's only pretending to be. It would be centrally focused on the character of Batman, it wouldn't get lost in a villain-of-the-week format, and it would meaningfully have resolved the dilemmas brought out over the first two movies.
Toy Story
Toy Story, even more than Star Wars, was not meant to have a sequel, and even Toy Story 3, as others have pointed out, is little more than a reskin of Toy Story 2. It's the same beloved characters getting up to the same old hijinks, but there's no pertinent narrative evolution between them, Andy's just not that important to the story.
Bourne
While the Bourne movies do have an over-arching plot, they're so frequently buried beneath their non-stop generic action scenes that they all begin to blur together very quickly, which is a very poor position to be in when considering the quality of a set of movies as an "iconic" trilogy.
The Godfather
Dollars
I've not watched all of these.
Surprised Back to the Future didn't make it on here. If it had, I'd have faulted it for it's black sheep third movie, which breaks from the formula far too heavily to comfortably gel with the other two movies.
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