I don't actually agree with some of them, but the following appear to be known for being better than the original.
Superman II (1980)
Aliens (1986)
Terminator 2: Judgement Day (1991)
The Godfather: Part II (1974)
Lord of the Rings: Return of the King (2003)
The Dark Knight (2008)
Mission Impossible: Ghost Protocol (2011)
National Lampoon's: Christmas Vacation (1989)
Star Trek II: Wrath of Khan (1982)
Toy Story 2 (1999)
10 Cloverfield Lane (2016)
Lethal Weapon 2 (1989)
The Godfather: Part II (1974) Both about equal. Wouldn't say II was better, though. The two mesh together seamlessly as one saga, which is the highest compliment you can give a sequel.
Lord of the Rings: Return of the King (2003) Yes. Each installment got successively better. On the other hand, it wasn't really a sequel. Tolkien himself submitted the entire LOR manuscript to the publishers before breaking it up into three parts.
The Dark Knight (2008) Maybe. Not a fan of the Nolan Batman's though, tbh.
Mission Impossible: Ghost Protocol (2011) Couldn't care less. They're all pretty mediocre.
National Lampoon's: Christmas Vacation (1989) Possibly, although the fact that this film is a holiday time staple may color people's judgment a bit.
Star Trek II: Wrath of Khan (1982) Overrated. I've always considered Star Trek: TMP a vastly UNDER-rated film.
Toy Story 2 (1999) Not seen.
10 Cloverfield Lane (2016) Not seen.
Lethal Weapon 2 (1989) Not seen
***Mad Max II: The Road Warrior was so good that it almost makes the first film (which was also pretty good) seem redundant an unnecssary.
Mad Max was a wonderful little B-movie with great music, editing, direction, and yes, great stunts. It was basically a dystopia futuristic revenge Western set in Australia. The Road Warrior took the mythic Western vibe even further, with a stranger-rides-into-town-and-saves-the-settlers-before-riding-off plot. And the action scenes were even more spectacular. The subsequent Mad Max movies abandoned the Western overtones, and I think suffered for it.