Odd bit of trivia regarding the original Die Hard that you can use to impress your friends. The film was adapted from a novel titled Nothing Lasts Forever by Roderick Thorp, which was a sequel to an earlier Thorp novel titled The Detective. The latter was adapted into a 1968 movie of the same name, starring Frank Sinatra. You can't say that Sinatra and Bruce Willis are playing the same character, but they're playing characters based on the same literary character, anyway.
Most of the character names were changed in Die Hard, although the leader of the gang in the book also has the last name Gruber. One major difference is that in the novel, Gruber really is a terrorist (I haven't read the book, but I think I the movie's change was a great idea).
I guess I like DIE HARD II more than you guys, as I think it's a remarkably enjoyable sequel, especially since it came out around the same time as some seriously shitty follow-ups like ROBOCOP II and ANOTHER 48 HRS. (Or sequels that were okay, but annoyingly changed the rules of the first film -- like LETHAL WEAPON II.)
But what I really like about DIE HARD II is that characters reference the fact that John McClane has become well known as a result of his actions in the first film. Someone says something like "You were a little out of your depth on Nightline." This never happens! (And isn't re-visited in the other films, where he's improbably down at heels.) I mean come on -- Jack Bauer would be a household name after what he does in the first season alone of 24, yet years later he's able to go undercover and no one recognizes him? That always bugs me.
For me, one of the deal breakers with Die Hard II is something Tom mentioned - that an plane full of British passengers is destroyed, on Christmas eve, no less, and forgotten about five minutes later (especially with the ridiculous "rip the parking ticket" ending).
I love the first Die Hard, but the one subplot that doesn't work for me is the one with the two bumbling FBI agents. Not only are they redundant (we already know the cops are incompetent - Al excepted), but their death in the helicopter is practically played for laughs, which rubs me the wrong way (it's at odds with the rest of the film, where the humor is bleak, not goofy). That's a minor flaw in a great movie, though. The plane crash in II is a similar flaw, only much, much worse, in a much much lesser film. Although at least there it's not a joke.