This is a topic that has a tremendous amount of significance to me. I really like sequels- even the ones that suck- because I love seeing how writers try to force an idea into another story, and how the story goes the next creative step than it’s predecessor. It’s like, if you sat and thought real hard about what would be done in Jurassic Park 2, you could figure out- hey, they have a bigger budget, so they throw in faster, bigger, scarier, smaller, more elaborate dinos of all type, the body count is bigger, more action scenes; and creatively, at the end, the dino gets loose in a big city! Of course that’s what the writers did- it’s just logical! But the movie sucked, as did JP3, but were entertaining nonetheless. 
I did some in-depth ‘research’ (lol) into the subject like 6 months ago. Here are my lists. Brace yourself!
**Sequels that Bettered/Equaled Original**
The Godfather Part Two
The Empire Strikes Back
Bride of Frankenstein
Babe 2: Pig in the City
Dawn of the Dead
Aliens
Terminator 2: Judgment Day
Spiderman 2
The Matrix Reloaded
American Pie 2
Evil Dead 2
The Gods Must Be Crazy 2
Hot Shots: Part Deux
Austin Powers: The Spy Who Shagged Me
The Road Warrior: Mad Max 2
X-Men 2
Toy Story 2
Bad Boys 2
Home Alone 2
Look Who’s Talking Too
Star Trek 2: The Wrath of Khan
**Sequels that Didn't Suck**
Back To the Future Part 2
Terminator 3
The Matrix Revolutions
American Wedding
Army of Darkness
Austin Powers: Goldmember
Rambo: First Blood Part Two
The French Connection 2
Scream 2
Scream 3
Friday the 13th Part 2
Phantasm 2
Die Hard 2
Die Hard With a Vengeance
Ace Ventura: When Nature Calls
Shanghai Knights
Rush Hour 2
Charlie’s Angels: Full Throttle
Mission: Impossible 2
Superman 2
2010
Lethal Weapon 2
Wayne’s World 2
Ringu 2
Ringu 0
Halloween: H20
Indiana Jones and the Last Crusade
2 Fast 2 Furious
Blade 2
Blade: Trinity
Tomb Raider: Cradle of Life
Scary Movie 3
The Bourne Supremacy
Ocean’s Twelve
The Mummy Returns
Teenage Mutant Ninja Turtles 2: The Secret of the Ooze
Red Dragon
Lethal Weapon 4
The Nutty Professor 2: The Klumps
Child’s Play 2
Shrek 2
Addam’s Family Values
Bill and Ted’s Bogus Journey
Father of the Bride Part 2
Naked Gun 2 ½
A Better Tomorrow 2
Hannibal
The Chronicles of Riddick
Bridget Jones: The Edge of Reason
Before Sunset
Desperado
The Princess Diaries 2: Royal Engagement
Dr. Doolittle 2
Meet the Fockers
The Santa Clause 2
Legally Blonde 2
West Craven’s New Nightmare
Innocence: Ghost in the Shell 2
Bride of Chucky
Seed of Chucky
Gremlins 2
Scooby Doo 2: Monsters Unleashed
Stuart Little 2
Spy Kids 2: Island of Lost Dreams
Spy Kids 3D
Analyze That
Barbershop 2: Back in Business
Highlander 2: The Quickening
My Girl 2
D2: The Mighty Ducks
Agent Cody Banks 2: Destination London
Police Story 2
Samurai 2
Samurai 3 (Musashi Miyamoto trilogy)
Jack Frost 2: Revenge of the Mutant Killer Snowman
Pokemon 2
Carnosaur 2
Carnosaur 3
Lone Justice 2
Escape From the Planet of the Apes
Conquest of the Planet of the Apes
Battle for the Planet of the Apes
The Karate Kid 2
The Next Karate Kid
Major League 2
Alien Resurrection
Alien vs. Predator
Once Upon a Time in Mexico
Robocop 2
Robocop 3
Porky’s 2
Porky’s 3
Death Wish 2
Batman Returns
Sequels that are Foreign Films, the IMDB has no info on them, but I list them b/c they SOUND like they could be good (that’s just nuts)
Eternal Regret, Part 2
Time and Tide 2
Rights from the Heart Part 2
Shadow Warrior 2
Family 2
Dissolute Wife 2
Polygamy 2: The Final Clash
Covert Operations 2: The Search for Justice
Human Market 2: Burning Desire
Yeong-ja in Her Prime 2
Terrorist 2
The Judas Kiss 2
Prodigal Boxer 2
Sword and 9 Rings, Part 2
Palace of Evil, Part 2
Dead 2: The Skull of Pain
Heartless 2
Counter Attack 2
Crossover 2
Scorpion 2
Days of Betrayal 2
Fatal Exposure 2
Wedding Dress of Tears 2
Who is Not Romantic? Part 2
Way of the Dragon 2
Kung Fu Hero 2
Whew! Look, these entries are, well, some of them violate your rules, some of them are just plain wrong by most people’s standards, and I haven’t seen probably 40%- and from reading the list, you’d think I have a bias for crappy modern films. I’ve seen a lot of the good stuff, I just made this list with some kind of a skew, didn’t I?
I mean, how can I call Bad Boys 2 a superior sequel when the original was complete rubbish and it is nothing but eye candy? :rolleyes:
But I did a good job of reviewing most of the notable sequels ever made! I went to the IMDB and typed in ‘2’ in the search box. It brought up thousands of entries, almost all sequels. So I looked through many many many pages. I did a pretty good job, and that explains where that last column comes from! 