Anime films I recomend:
"Grave of the Fireflies", "Barefoot Gen": You MUST see these two if you want to be a real otaku, but I must warn you, it's a one way ticket to depressionville. "Grave..." is the only movie that really made me cry.
"End of Evangelion" and "Cowboy Bebop - Knocnking on Heavens Door", but do watch their respective series first
"My Neighbor Totoro", "Porco Rosso", "Nausicaa", "Spirited Away" - from Ghibli Studios (not sure if Porco Rosso is).
"Wings of Honeamise", "Otaku no Video" (not sure of the american or japanese title) - early ones from Gainax, must-see.
"Akira" and "Ghost in the Shell", obviously. Maybe "Steamboy".
Osamu Tezuka's Phoenix saga movies, Osamu Tezuka's Metropolis.
If you WANT stick to convencional, popular animes, try the "Bardock TV special" from DBZ (the only thing from DBZ universe that's really worth watching), the Naruto film, the Rurouni Kenshin movie, maaaaybe one of the "Saint Seiya" movies...