Another really awesome movie that has a similar feel as the Matrix is:
www.manga.com/ghost
"A movie that questions our own human existence in the fast-paced world 
of the information age, this remarkable, award-winning, cyber-tech thriller has gone on to become one of the leading Japanese animation films of all time... Seamlessly merging traditional cel animation with the latest computer graphic imagery, this steming sci-fi spectacle has broken the boundaries of mainstream animation with its detailed artistic direction and uniquely inteligent story line." - DVD Back Cover
Ghost in the Shell is a Japanese Animé feature 
length film made in 1996 that some friends of mine (the same ones whom I went to the Matrix with) and I saw for the first time at a December animé show. While I was extremely tired at the time, I found the movie strangely awesome for being in Japanese and having to read the annoying subtitles. Now I warn you, I've seen an English movie dubbed to French and a Japanese cartoon dubbed to English, both of them totally lost the feel of the movie by having the voices changed. I highly recommend the subtitled version, even though it can be hard to get used to at first.
So what is this "Ghost"? In this future, somewhere in the early to mid 21st century, the world of information has virtually overtaken the world we know. The movie deals with much of the same issues that The Matrix does such as what defines a person; what makes us who we are, and what is real or what is life? I am not even going to begin to go into all the countless visual similarities for now. Maybe some time in the future though... :)
