Jeffrey at 2008-12-31 14:07:00:
One more for your list, Scott. The terribly overlooked Coen Brothers flick THE HUDSUCKER PROXY. As much as it's a totally daffy slapstick farce, it also addresses, quite touchingly, our collective choices and the passage of time and second chances.

"Y'know... for kids!"
Jeffrey at 2008-12-31 14:09:00:
Oh, and I forgot to add, one of the few films where the stroke of midnight on New Years Eve is a major plot point.

Additionally, the not-great-but-interesting STRANGE DAYS also uses New Years Eve to great dramatic advantage.
OutOfContext at 2009-01-01 13:01:00:
One of my favorite movies of all time, "Radio Days", ends with much of the cast on the roof of a building on New Year's Eve.