@SVX, watch anything and everything Studio Ghibli have made, all though you shouldn't feel in a rush to watch Tales From Earthsea or The Wind Rises as they're certainly below their usual par. Spirited Away usually serves as their best film to start with, but both the double feature of Grave of the Fireflies
followed by My Neighbour Totoro is also a good way in. Laputa: Castle in the Sky, Kiki's Delivery Service, Porco Rosso, and Princess Mononoke are all also completely awesome, but as I say, even if something isn't one's usual cup of tea, Ghibli will probably be able to make it one's cup of tea.
Cowboy Bebop. Coooooowboy Beboooooooop. Cowboy Bebop. Easily the anime series I would recommend the most. Not the best I've seen, but it's accessibility and downright awesomeness mean it goes highly recommended. It's a noir space western with martial arts movie elements and a (primarily) Jazz soundtrack. Oh, and it's one of the few anime where the American dub doesn't suck and the movie follow up has probably the best animation of anything, ever. That's all one needs to know.
Madhouse have made some great films, all though their output overall is a bit of a mixed bag; but The Girl Who Leapt Through Time, Summer Wars, Wolf Children, Redline*, and anything the late Satoshi Kon directed are all films worth checking out. Death Note is rather good too, so long as one can accept the inconsistency in the main villain's characterisation.
Akira is Akira. Most people probably wont like it, it's a weird movie, but it's just a film so one may as well watch it if they have the time, as if you can get into it it's well worth the watch. My Dad was inexplicably at the première, which means I have a sort of personal connection to it.
Puella Magi Madoka Magica is a masterpiece, albeit one that's accessibility is depleted by its (brilliant) but unusual visual style combined with a perhaps slightly over the top pastiche of the magical girl aesthetic in its character designs. (Oh yeah, and a horribly misleading opening sequence). But none of that can take away from the fact that its just a fantastic piece of storytelling that one should go into spoiler free the first time, but will then enjoy even more the second time when they already know how things play out. The best anime I've seen? I'm not sure, but my head would certainly tilt towards it.
Finally there's FLCL. FLCL is surreal. Extraordinarily surreal. And fast paced. Seriously, it crushes about 30 episodes of content into just six. But, when one goes back and rewatches it two or three times, the genius of how it summarises what it is like to be a twelve year old boy emotionally will start to shine through. Again, another masterpiece.
Don't watch Evangelion, you'll just be sucked in and eaten whole and waste eight months of your life that you'll never get back obsessing over whether or not Gendo's smile in episode 21 means he was actually a good person all along or whether or not Shinji's actions in End were justified by his mental state and stuff like that. It's awesome, but you should avoid it like the plague.
I figured it was like a manga, whoops.
