Seriously Good Sequels

There is a general rule in the movie world: sequels will be terrible.  It doesn't seem to matter how good the first film is, the sequel is almost guaranteed to be awful.

The Matrix was a great action movie.  It had a bit of philosophy, mildly decent writing, and fantastic special effects that moved the film along.  The sequels were boring, pretentious, and even the action was bad because the story was so awful no one cared.

Pirates of the Caribbean: the Curse of the Black Pearl was fun and engaging, funny, with wit and great action.  The sequels were among the worst blights that Hollywood has ever produced (including the fourth, which I look forward to ripping into in its own review).  They were not funny, they recycled lines and jokes, and they simply seemed to forget what made the first one great.

I could go on, obviously, but I'm interested in the movies that break the trend.  What sequels are just as good, or even better, than their predecessors?  Here are a few I love:

Terminator 2: Judgment Day
The first Terminator was your straight sci-fi film about a robot sent back in time to kill a teenage girl.  It had one good line ("I'll be back!") and some seriously awful stop motion animation.

T2 rose above the first in every way.  The writing was excellent, delving deeply into the hypothetical conundrums of time travel.  Is the future set, or is there "No fate but what we make?"  The acting was...well, the acting wasn't important.  It's a good movie in spite of the acting.  Most importantly, T2 showcased its special effects, using computer animation for the first time to make a enemy who could shape shift at will.  T2 is by no means a Best Picture oscar contender, but I love it.

Aliens
Alien was a haunted house in space.  It was all that feeling of being trapped in a tight space with a terribly powerful and frightening monster.

Aliens was something else entirely.  Aliens was about a war, where the aliens were killable but they just kept coming.  On a whole the movie is well-crafted, but the characters of Ripley and Newt stand out.  Sigourney Weaver actually was nominated for an oscar for her performance!  Aliens is a great movie -I still like Alien better, but Aliens takes the series in a new direction without compromise on quality.  That makes it great.

The Godfather, part II
The Godfather is one of the most iconic, most perfect movies ever made by Hollywood.  Practically everything in it screams quality and nearly every line is quotable.

Part 2 is just as good.  Leaving conventional storytelling, part 2 tells two tales at once, weaving the plotlines together.  On the one hand you have the continuing story of Michael Corleone as he transforms his family business into something much more powerful and sinister.  On the other hand you learn the story of Vito Corleone as he builds the empire his son will later take over.  As you watch you see the respect for Vito grow as his family does, at the end seeing how he is surrounded by loved ones and living his dream.  At the same time you see Michael alienate nearly everyone, ending up utterly alone.  This is not a movie you watch to be reassured of the pleasant side of life, but it deals with the dark nature of humanity head on.  And there is no denying its greatness.


So what do you think?  What are your favorite sequels, those that meet or surpass the original in quality?