From top to bottom:

LOTR: Fellowship of the Ring - one of my favorite movies of all time.
Memento - also one of my favorite movies and if you haven't seen it I seriously recommend it.
Harry Potter: Philosopher's Stone - love it.
Ocean's Eleven - great film.
Shrek - I like it, great animated feature.
Monsters Inc - same as the above.
Pearl Harbor - I have only seen this once, but I remember really liking it.
Training Day - Denzel Washington is very good in this, I like it.
Black Hawk Down - lots of explosions with people shooting at each other, I like it.
I Am Sam - I want you to kill. Kill. KIIIIILLLLLLLLL. Yeah, I like this one.
The Fast and the Furious - For a street racing film, it was very good. But this isn't really my type of film.
Artificial Intelligene: AI - Yeah, it was okay.
Hannibal - It was okay, but nowhere near great.
Vanilla Sky - I really didn't like this film.

Two films I need to give a second try (mostly the former), they were way too weird for me at the time so I haven't been able to appreciate them. Bill Murray ftw though.
Donnie Darko
The Royal Tennenbaums

Two films I haven't seen that I need to see someday are A Beautiful Mind and Moulin Rogue. Some of the people I knew back in 2001 who were into musicals were like what!? you haven't seen Moulin Rogue. Why!?

Mudholand Dr... never even heard of it. Is it good?

The Royal Tennenbaums and Donnie Darko are strange movies so I'll probably give this other strange movie a peek sooner or later.