Angelic Layer
Azumanga Daioh
Chobits
El Hazard
*Golden boy
Haibane Renmei
Hand Maid May
Mahoromatic series 1+2
Tenchi (Muyo is best, but Universe and Tenchi in Tokyo are still good)
*Those Who Hunt Elves 1+2
Video Girl AI
Witch Hunter Robin
Wolf's Rain
X (TV)
Ayashi no Ceres
I My Me Strawberry
*Kiddy Grade-
*Najica Blitz Tactics (good, but very OTT with upskirt panty shots, almost to the point of being TOO OTT)
*Outlaw Star
*Raimuro senkitan (be careful of the bum waving maracas in the outtro)
*Saikano
*Scrapped Princess
violinist of hamelin
Piano
Noir
*Slayers
*Escaflowne
*Lain (be careful)
*Now and Then, Here and There (Dont let anyone interrupt you)
Trigun
films:
Laputa castle in the sky
Metropolis
tonari no totoro
grave of the fireflies (must see, but dont let anyone interrupt you or it'll spoil the atmosphere)
perfect blue (must see)
any other film done by "studio Ghibli"
i think there's enough there to last you a year without ever having to watch anything other than anime
also, i apologise for the changes in alphabetic order, i had to change hdd browsing and also dvd/cd/vhs collections
and most of these fit into the catagory of not being martial arts (TWHE has karate man, but it's mainly a comedy series)
the * titles are ones that fit closest to your preference, but ALL of the others are still worth watching. many of them are cute schoolgirl/love/AI love stories, comedy, or a mixture of everyhting (which is what makes anime great)