Ill just throw up a few that have def made an impact on me. I've had a love affair with Anime since the early 90's back when this syndicated channel (i think it was syndicated) use to show anime every fri and sat night at like midnight. I was exposed to Wicked City, Vampire Hunter D, Barefoot Gen, Doomed Megalopolis (fucking heart this), among many other twisted anime, which i feel hasn't been replicated in a while although some have come close.
Record of Lodoss Wars - First VHS i ever bought and is probably the only Fantasy/Knights/Etc anime that i truely adore.
Serial Experiements Lain - First DVD i ever bought, love it and the music dearly.
Studio Gainax - i dont really know what they've done recently but FLCL, Neon Genesis Evangelion, Royal Space Force: Wings of Honneamise, Gunbuster, Otaku No Video, Ebichu all are huge faves of mine.
Azumanga Daioh - one of the few (very few) cutiesy anime i like, this did make me shead a tear near the end. liked it so much i even got the giant "graphic novel" manga that collected all of the volumes.
Cowboy Bebop - i loved this series (minus the movie) it flowed really well had great and equal amts of drama, comedy etc. English Dub is fantastic.
Barefoot Gen - made me cry when i first saw it.
Blood The Last Vampire - a little overrated but still an enjoyable short. never got around to watching the Blood + series.
Blue Sub 6 - excellent and a wonderful ending to boot. animation is beautiful
Boogiepop Phantom - dunno what to say about this doesnt make a whole lot of sense but usually the fucked up ones dont :)
.hack//sign - this series to me is leagues beyond all of the other .hack franchises. the soundtrack is A+ material and the story is beautiful.
Satoshi Kon - anything by this fucked up individual - Perfect Blue, Paprika, Millennium Actress, Paranoia Agent, Tokyo Godfathers.
All of the anime by Makoto Shinkai has made me cry - She and Her Cat, Voices of a Distant Star, Place Promised in our Early Days and 5 Centimeters Per Second this is without a doubt my fave anime ever, it hit me pretty hard to where i can't watch it again, it makes me that sad.
Iria - :) sci-fi
Excel Saga - i recommend the first half of the series, makes me laugh everytime.
Now and Then, Here and There - very touching story that spans time and space
Planetes - funny, dramatic where the main characters are space garbage collectors.
Gantz - decent and entertaining
Macross Plus - dunno if it was the combination of the ending plus the ending music but made me sad, great OVA.