Some favorites off the top of my head, no particular order:
Inuyasha
Fullmetal Alchemist
Cowboy Bebop
Trigun
Girls Bravo (in a way)
Avatar: The Last Airbender (I know it's not of Japanese origins but the style is there, that's good enough for me)
Eyeshield 21
Haruhi Suzumiya/Yuki Nagato spinoff
Bleach
Monster Musume
Abenobashi
FLCL
Currently watching:
Ika Musume
Umaru-Chan
One Punch Man