Here are sequels that I liked as much or better than the original.
Addams Family Values
Aliens (one of my favorite movies of all time)
Goldfinger
The Bourne Supremacy and The Bourne Ultimatum
Die Hard 2 and Live Free or Die Hard (maybe not as great but I really like both of these entries in the series)
Fantastic Four Rise of the Silver Surfer (even with the flaws it is an enjoyable movie)
Harry Potter and the Prisoner of Azkaban and Harry Potter and the Goblet of Fire (my favorite two in the series)
Mission Impossible 2 and Mission Impossible 3 (enjoyed both of these much more than the original)
Ocean's Thirteen (closer to the greatness of Eleven than Twelve)
Rugrats In Paris (go ahead and laugh but this is one funny movie)
Spider-Man 2 (my favorite of the three)
Star Trek II: The Wrath of Khan and Star Trek First Contact (my favorites of the bunch)
Star Wars: The Empire Strikes Back
Tomb Raider: The Cradle of Life (I really enjoyed this one better than the first one)
X-Men 2
Addams Family Values
Aliens (one of my favorite movies of all time)
Goldfinger
The Bourne Supremacy and The Bourne Ultimatum
Die Hard 2 and Live Free or Die Hard (maybe not as great but I really like both of these entries in the series)
Fantastic Four Rise of the Silver Surfer (even with the flaws it is an enjoyable movie)
Harry Potter and the Prisoner of Azkaban and Harry Potter and the Goblet of Fire (my favorite two in the series)
Mission Impossible 2 and Mission Impossible 3 (enjoyed both of these much more than the original)
Ocean's Thirteen (closer to the greatness of Eleven than Twelve)
Rugrats In Paris (go ahead and laugh but this is one funny movie)
Spider-Man 2 (my favorite of the three)
Star Trek II: The Wrath of Khan and Star Trek First Contact (my favorites of the bunch)
Star Wars: The Empire Strikes Back
Tomb Raider: The Cradle of Life (I really enjoyed this one better than the first one)
X-Men 2