Robotech (generations 1 and 3)
Macross Plus: Episodes and the Movie
Rurouni Kenshin: Seisouhen (OVA 2)
Record of Lodoss War
Neon Genesis Evangelion
Princess Mononoke (Mononoke Hime)
Grave of the Fireflies
Mermaid's Scar
Battle Angel/Gunnm
Lain
Aa! Megami-sama! (Oh! My Goddess!)
Fatal Fury: Legend of the Hungry Wolf and the Motion Picture
Street Fighter II V (Victory)
Street Fighter Alpha
Street Fighter: The Animated Motion Picture
Ranma 1/2
Please Save My Earth (Manga)
Weiss Kreuz (Manga...although I've seen tidbits of the anime!)
Fushigi Yuugi OVA Series
Ghost in the Shell
Ninja Scroll
Vampire Hunter D: Bloodlust
Ayashi no Ceres
Love Hina
Dragonball (Z, GT, the 1st season...all of them)
Ronin Warriors/Samurai Troopers
Teknoman/Tekkaman Blade
Laputa: The Castle in the Sky
Tenchi Muyo
Bishoujo Senshi Sailor Moon Super: The Movie
Bishoujo Senshi Sailor Moon R: The Movie
Nadeisco
Tenkuu no Escaflowne: The Movie and Series
Card Captor Sakura
Outlaw Star
Yuu Yuu Hakusho
Flame of Recca
Akira
Project A-Ko
Legend of the Five Rings (this isn't an anime, but it's a cool book
series based on myths from Japan, China and Korea)
Appleseed
Battle Arena Toshinden
Blue Submarine No. 6
The Cherry Project
Clover (Manga by CLAMP)
Dangioh
Dirty Pair Flash
The Guyver
Raven Tenguu (sp?) Kabuto
My Neighbor Totoro
Nausicaa: The Movie
Ninja Cadets
Samurai Pizza Cats
Ninja Turtles
Tekken: The Motion Picture
Those Who Hunt Elves
Vandread
Voltron
Trigun