Boku no--I mean, uh...
Movies/OVAs:
Princess Mononoke, Time of Eve, Blood: The Last Vampire (If you're going to watch Blood+, watch B:TLV first), Spirited Away and Hellsing Ultimate (the original's good, but I, personally, think the manga story is more coherent).
Series:
Mononoke (it's something different, trust me), Serei no Moribito, Last Exile, Kemonozume, Haibane Renmei (shut up), Serial Experiments Lain, Dennou Coil, Mushishi, Fullmetal Alchemist: Brotherhood (see my caption about Hellsing Ultimate), Baccano!, Durarara!! and, uh... Monster.
All of these are highly recommended by me, but Princess Mononoke, Blood, Moribito, Lain and Dennou Coil are not to be missed. Monster's really good, but it gets kinda slow at times. I tried not to name stuff that I knew other people would mention or that might be super mainstream, so if I did (like with FMA and Moribito, for example), it's because they're just that good.
Edit: Oh yeah, Soul Eater, too. I'd put that and FMA up in the top tier of shounen anime. Good production values and actual plots. Though Soul Eater does like to lean towards the disjointedness of its shounen brethren from time to time aaaand Black Star is effectively Naruto... Airmaster is also worth mentioning for its simplicity, if nothing else. It doesn't have a real story outside of "Maki likes to break bones," but it also doesn't pretend to be anything more than it is.
More edit: I'd also recommend checking out some manga, too. Blame! and Uzumaki are probably higher on my list of favorites than just about every anime I've seen. 20th Century Boys (by the guy behind Monster) and Historie are awesome, too. Oh, oh, and Basilisk. The manga is great and the anime is beautiful.