Cels Forum

Depends on what you like.  Anime isn't a genre, it's a medium
with many genres.  Here are some recommendations for various
genres...

Romantic comedies:
Kimagure Orange Road
Video Girl Ai
Marmalade Boy
Maison Ikkoku
Ah! My Goddess
Koko wa Greenwood

Comedies:
DragonHalf
Ranma 1/2
Golden Boy (not for young viewers)
Yawara

Science fiction:
Gunbuster
Battle Angel
BubbleGum Crisis
Evangelion

Fantasy:
Nausicaa
Laputa
Escaflowne
Lodoss Wars
Fushigi Yuugi

Action/Adventure:
Ninja Scroll
Golgo 13
Crying Freeman

Drama:
Grave of the Fireflies

Romance:
Whisper of the Heart
Omoide Poroporo
I Can Hear the Ocean (Umi ga Kikoeru)

Other:
Kiki's Delivery Service
Totoro
Utena
Please Save My Earth