I was recently browsing lists of the best movies of all time. Movies
like Citizen Kane and Lawrence of Arabia tend to top these sorts of
lists. It's fascinating to think about what factors make a movie a
classic for many years. And it made me wonder: which movies released
in the past few years (lets say since 2000) will become classic movies
of this sort and remembered 50 years from now? When I looked around
for this info, the best I could find were a few threads on "best
movies since 2000" - this feels different from the movies most likely
to be rememebered and become classics. Thank you for your opinion.

This may be of interest to you:

http://chasingthefrog.com/forums/archive/index.php/t-1116.html

There aren't any!

They've stopped making potentially 'classic' movies because they no
longer have true stars, great scripts or imaginative directors.

I am hopeful that "Bladerunner" will endure; it's doing okay so far
(and will be re-released in theaters soon!). I am fearful that
"Titanic" will be the "Casablanca" of the 1990s.

Recent movies I'll recommend to my great-grandchildren:

A.I. (like everything Kubrick touched, this is a masterpiece)
Napoleon Dynamite (or Peluca)
Harry Potter 1 and 2
C.S.A. (very creepy)
Everything is Illuminated
Last King of Scotland (Whitaker is brilliant, everything else is so-so)
The Matrix (will they laugh at it as we do at old Ray Harryhausen effects?)

I see a lot of movies, and have to say in my personal opinion A
Beautiful Mind was hands down the best - worthy of enduring
appreciation.  A couple of movies that are a bit older that were well
done are The Princess Bride, and Shawshank Redemption.

I would say Elf will go down as a holiday classic, I think it will age
well.  Also LA Confidential and Amile.

my favourites are mission impossible 3 and enter the matrix.brilliant movies!!!

ironclaw-ga ... 

Mission Impossible 3 ... Are you SERIOUS?

I saw MI-1 (which was awful); my daughters saw MI-2 (which was worse)
and I hear that MI-3 is the pits.

You must be either Tom Cruise or his Publicity Agent ...

C'mon give us a clue.

I would say that introducing a new concept in movies would make it a classic. 

Lord of the Rings series is a given.
The Spider Man series was well-made and could come in. 
Gibson's The Passion, maybe? 
Disney's The Incredibles is one for cartoons. 
Howl's Moving Castle might be a contender. 
I predict Transformers next year might come into the picture...