I would put Godfather, Part II at the top of the list as well. At the very least, it's the only sequel to a Best Picture that equaled or surpassed the original (how does The Evening Star, French Connection II, or The Sting II strike anyone?). And it's not quite the same as The Lord of the Rings, because LOTR was filmed all at the same time, and everybody knew from the beginning that the next installment would be a simple continuation. The Godfather was not made with any presumption that another movie would follow.

As far as others go, the best sequel for me would be The Road Warrior (Mad Max 2). I thought that the original Mad Max had some good moments, but was a flawed movie overall. The Road Warrior surpassed the original in every facet by not trying to rehash the original premise, but advancing it far enough ahead in time so that a very different world and thematic interpretation could be created. It remains one of my all-time favorite movies, sequel or not.

Another personal favorite sequel that not too many other people liked would be Gremlins 2, which dispensed with the quasi-horror elements from the original (BTW, I did not like the original Gremlins) and went entirely in a cartoonish satirical direction with the sequel. Though a lot of the satirical references in that movie don't hold up well over time, that movie had a sense of fun, abandon, and refreshing lack of self-importance about it that I don't see with a lot of sequels. For example, I don't know of any sequels that would do something like including a cameo from film critic Leonard Maltin where he hashes over how much he hated the original movie.

T2, Aliens, and The Wrath of Khan are other very good ones that others have mentioned.

The Washington Post recently had an article detailing how The Road Warrior is the best example of how to create a sequel that surpasses the original.

http://www.washingtonpost.com/wp-dyn...900331_pf.html

P.S. This list is contingent on the fact that I have yet to see Debbie Does Dallas 2!