The Ghibli movies (Nausicaa, Cat Returns, Porco Rosso, Pom Poko, Kiki's Delivery Service, Laputa: Castle in the Sky, Howl's Moving Castle, Princess Mononoke, My Neighbour Totoro, Grave of the Fireflies, Whsiper of the Heart, My Neighbours the Yamadas, Spirited Away, Only Yesterday) are usually dirt cheap and a good enough starting point, applicable to most tastes. Add The Castle of Cagliostro to that list too (it's an earlier film by Ghibli director Miyazaki, but seems to hit a chord with people not too fussed about Ghibli films). Aside from that, Dave has got most of the bases covered already. I'll mention Macross Plus as well, on the off chance that robots beating each other up and hideous Manga Entertainment packaging aren't detrimental to your enjoyment of a good action movie/OAV. Oh and Akira, since even I feel obliged to mention such an old cliche when others leave it out (Personally, I think it's mediocre, but not having an opinion on it is a bit like being part of a film-club and not having seen 2001: A Space Odyssey or something).