Worst: Highlander II, Godfather III, Robocop III, Jaws: The Revenge, Exorcist II, All the Death Stalker Sequels
Best: Exorcist III, Godfather II, Friday the 13th Part VI, Rocky IV, Aliens, Evil Dead 2, Police Story 3, Bride with White Hair 2, Swordsman 2, A Chinese Ghost Story 2 and 3
The Highlander II was my introduction to bad sequels. And I don't think any sequel has topped that as my worst viewing experience. Robocop III is a close second to that. The original Death Stalker wasn't that good at all, but the sequels are an abomination, reusing more and more footage to pad the run time and only be entertaining because they are so bad its good kind of movies.
For best sequel, my personal favorite is Exorcist III, which was was such a pleasant surprise when I first saw it, but which has stood the test of time over repeat viewings through the years. Evil Dead 2 was superior to the original and a genuine classic. Friday the 13th Part 6 elevated the franchise and is better than any of the films that came before it in that series, Godfather II is somewhat obligatory (I still prefer part one but 2 is very good). Police Story 3 is an amazing entry in that franchise. Bride with White Hair 2 doesn't touch the original but it is still wildly entertaining. Didn't know Swordsman 2 was even a sequel because when it first came here it was just called Legend of the Swordsman, but having seen the whole trilogy since then, it is without doubt the best entry. Nothing beats the perfection of Chinese Ghost Story but the two sequels are worthy installments