I took some liberties with these recommendations, but it's all candy. 90% of the are great, the rest 10% just very good that I liked a lot. Watch them all or die trying.
dying is not an optionBlack Cat (very typical shounen action, but I actually liked it)
Cowboy Bebop (space adventure classic, soundtrack by Kanno Youko!)
Darker than BLACK (one of the best action anime of the decade, the second season sucks though, soundtrack by Kanno Youko!)
FLCL (hyperactive mecha parody)
Gin'iro no Kami no Agito (anime film, post apocalyptic)
Gunslinger Girl (girls as assassins, in Italy)
Kaiba (one of my favorites, nothing like you've ever seen before, it's unique and it's awesome)
Kaidoumaru (ova, set in Heian period, visually attractive, nice music, one of the best animes set in historical Japan)
Kaze no Tani no Nausicaä (Miyazaki's post apocalyptic classic, music by Joe Hisaishi!)
Kino no Tabi (kinda philosophical, travel's of Kino and a motorcycle Hermes—some action)
Kumo no Mukou, Yakusoku no Bashou (Shinkai's scifi film, music by Tenmon)
Last Exile (steampunk anime about two pilots)
Megazone 23 (three part ova, cyberpunk classic, I like the first part the best)
Memories (three part ova, scifi classic, first is drama, second comedy, third?)
Metropolis (movie, based on a classic manga)
Mezzo Forte (two part (?) ova, mercenary team)
Mind Game (hyperactive surreal adventure, by the maker of Nekojiru-sou(look below))
Nekojiru-sou (surreal adventure of a kitten to save his sister, who lost her soul, if you've ever watched the original Nekojiru series—this is totally different)
Neon Genesis Evangelion (new mecha classic, and if you're interested in mecha, try other Macross too, and Gundam)
Noir (gunslinger girl -like feeling, assassins in france)
Otogizoushi (intepended? sequal to Kaidoumaru, second half set in modern day)
Paprika (scifi mystery, based on a novel)
Sen to Chihiro no Kamikakushi (Miyazaki's, music by Hisaishi)
Serial Experiments Lain (cyberpunk, psychological thriller, mystery, philosophical themes, a classic,)
Tenkuu no Shiro no Laputa (old one by Miyazaki, music by Hisaishi)
Texhnolyze (same kinda feeling as with lain, more violent)