Movies......
Akira
Spriggan
Silent Mobius Motion Picture 1 and 2 (good luck finding that one)
Appleseed (2004 version)
Ghost in the shell
Patlabor Motion Picture 1, 2
Any thing by Studio Gibli. However you either love it or not interested in it.
Dead Leaves
Sadly most of the other anime movies out their really require you to have some knowlegde of the TV series or a managa series. Or they are just rather disappointing when you compair them with the TV series or manga.
Like I never really liked akira until they released the books into english a few years back.
Appleseed as so much more to tell manga. However they are doing another movie which is going to be out next year.
Ghost In The Shelll Motion Pictures are a good little introduction to the series. However the Ghost In The Shell Stand Alone Complex TV series is so much better.
Apart from that, most of the movies that are out there really only act as high budget episodes for TV series given a theactical release. Most of the time I watch the movies, and I am more or less disapointed due to the lack of character development that we are used to seeing in the TV series.
Otherwise, you can have a look at some of the OVA series that are out there.