Patlabor
Patlabor 2
Wings of Honneamise
Anything by Studio Ghibli
Nausicaa of the Valley of Wind
Castle in the Sky
My Neighbour Totoro
Grave of the Fireflies
Kiki's Delivery Service
Only Yesterday
Porco Rosso
Whisper of the Heart
Princess Mononoke
My Neighbours the Yamadas
Spirited Away
Howl's Moving Castle
Try the Ghibli films. Or try some wuxia series (not films). Try the 2003 adaptation of She Diao Ying Xiong Zhuan (Eagle shooting Hero), 42 episodes long, whose early parts contain a interesting look at the Mongol way of life. In short, don't judge until you've seen the better examples of the culture - Miyazaki himself said that 90+% of all anime is pure garbage, but it'll be silly to lump him in with the others.