A few recomendations with brief comments.
Perfect Blue - Psychological thriller about a pop star turned actress who gets to celebrate her new career with a stalker and a mental breakdown. This would work fine as a live action film, but being animated helps keep the line between reality and the fantastic blurred - not to mention it's stylish as all hell.
Millennium Actress - A love letter to Japanese cinema circa the mid-30s through the mid-60s, as an aging star reflects on her life to a couple of hapless documentarians who find themselves reliving her films and memories. Where the shifting realities in Perfect Blue are ominous and disturbing, here they're nostalgic and glorious to behold. Simply beautiful, and with one helluva soundtrack to boot.
Tokyo Godfathers - A retelling of the classic, oft-reworked
Three Godfathers, wherein three bums in Tokyo - a drunk, a transvestite, and a teenage runaway - find an abandoned baby and try to return her to her parents. Wacky hijinx ensue, as our heroes encounter mobsters, street gangs, family members, and the occasional bit of Christmas magic. Wonderful fun!
What? I should recommend something other than Satoshi Kon flicks? Fine, fine.
Castle of Cagliostro - All of Miyazaki's flicks are great - if you haven't seen it yet, see if Howl's Moving Castle is still in theatres near you - but, if cornered, I'll peg Cagliostro as our favorite. The loveable Lupin gang (with Lupin III as their lecherous leader, Jigen as the crackshot second, Goemon as a sword weilding samurai gone crooked, and femme fatale Fujiko) find themselves rescuing a princess and discovering a hidden treasure in one of the best adventure films, animated or otherwise, ever made.
Memories - An anthology film featuring adaptations of three short manga by Katsuhiro "Akira" Otomo: the beautiful "Magnetic Rose", wherein salvage astronauts answer a distress signal and find themselves in a baroque, operatic nightmare; "Stink Bomb", black comedy about a hapless pharmaceutical researcher who becomes a living chemical weapon; and the European-styled fable "Cannon Fodder", about a society and their endless war.
Cowboy Bebop: Knocking on Heaven's Door - Bebop really shines as a TV series (26 episodes on 6 DVDs), but if you want to get a taste for the show the movie is as good an introduction as you could ask for. It's 2071 and our heroes (Spike Spiegel, the martial artist with a dark past; Jet Black, ex-cop and long-suffering captain; Faye Valentine, all femme but not so much fatale; and Edward Wong Hau Pepelu Tivrusky IV, mutant prepubescent hacker) are interstellar bounty hunters struggling to keep food on the table. While the characters are great, the animation is lavish, and the plot is intriguing, what really makes Bebop shine is it's sheer, overwhemling amount of style. It is the embodiment of style, particularly in it's everything and the kitchen sink soundtrack. So, check out the movie, and if you like it start watching the TV series posthaste.
So, there you go. Six flicks, all readily available in the US on DVD, and a series to check out if you dig on these. If you tear through Bebop and find yourself wanting more, the creators recently completed the delightfully anachronistic Samurai Champloo, 26 episodes of hip-hop samurai ass-kicking. If you really liked Ghost in the Shell, start watching the 26 episode TV series Ghost in the Shell: Stand Alone Complex, which has one helluva budget, smart writing, and one helluva on-going plot in the Laughing Man storyline. And, if you're really hardcore, go rent Assemble Insert. Trust me.
FnordChan