Thought I'd share my own anime list for the rest of you guys to enjoy. There's a few overlaps but still a fair bit of unique ones!
Accel Work
Ah! My Goddess
Angel Beats!
Aria the Origination
Azumanga Daioh
Baka and Test (quite the hilarious anime)
Bakemonogatari
Bludgeoning Angel Dokuro-chan
Bokurano
Card Captor Sakura
Chaos;Head
Chobits
Chrono Crusade
Clannad (Don't watch if you don't like tearjerkers)
Clannad After Story (Tearjerk level: Clannad +100)
Code Geass (watch seasons 1 and 2, best plot twists, hand down)
Cowboy Bebop (see you, space cowboy. ;_; )
Darker Than Black (Season 1, Season 2, OVA Series)
Death Note
DN Angel
Fairy Tail (still ongoing, pretty fun and lighthearted shonen)
FLCL
Fruits basket
Fullmetal Alchemist (Original, a couple of OVA and Brotherhood; first anime I watched, got me hooked)
Future Diary
Genshiken
Ghost Hound
Ghost In the Shell
Great Teacher Onizuka (repeat from above but full name)
Haibane Renmei
Hajime no Ippo
Hand Maid May
Haruhi's Endless Hig
Hidan No Aria
Hyouka
Ichiban Ushiro no Dai Mao
Inuyasha
Kanon
Last Exile
Monster
Now and Then, Here and There
Omamori Himari
Ouran High School Host Club (I laughed pretty much the whole time, it's quite the experience)
Phantom: Requiem of Phantom (INTENSE)
Princess Nine
Rumbling Hearts (Meh, but still pretty good)
Rurouni Kenshin
Samurai Champloo
School Days (and the obligatory nice boat)
Scrapped Princess
Soul Eater
Special A
Speed Grapher
Steins;Gate (My head is full of "wtf," must-watch imo)
Tengen Toppa Gurren Lagann
The Melancholy of Haruhi Suzumiya
The Mightiest Disciple Kenichi
The World God Only Knows
Toradora!
Trigun
Welcome to the NHK!
Wolf's Rain
Zipang (watched this a long time ago, seems hard to find nowadays even on my computer)
Also, every movie by Hayao Miyazaki. Includes Kiki's Delivery Service, My Neighbor Totoro, Spirited Away, Howl's Moving Castle, Castle in the Sky, Princess Mononoke, etc, etc.