I'm surprised so many people enjoyed 'Spirited Away'. I watched in when I was living in Japan, and I really didn't "get" it. My parents tell me it's because there are so many references to classic Japanese myths and fairytales (I grew up in Canada so I wasn't exposed to them). THEY enjoyed it quite a bit, however. It was the same thing with all of my other Japanese friends though; they didn't enjoy it too much either.
'Kiki's Delivery Service' I really did enjoy, along with 'My Neighbour Totoro', 'Porco Rosso' and 'Nausicaa of the Valley of the Wind'.
Kiki I really enjoyed because, first, it's such a basic story; anyone can relate to it. Second, the characters are really innocent; for a couple of hours it acts as a great escape from our world. In that sense it's got the same charm as Buffy tVS. Kiki's real cute too.
Totoro: You gotta love those Totoro's they're so cute! Actually most of the characters in that were cute. Also there's an idylic feel to certain parts of the story that borders on being mystical.
Porco Rosso: I've never properly seen Europe, but this is the way I imagine it was 50 years ago. The scenery in this movie is just gorgeous. I'm also fan of air to air combat scenes so I have a natural weakness for this movie. Did anyone else feel like building a model of the Saviola S-2 after seeing this movie? Fantasy people have to love the sense of valour, and Fio's kinda cute too.
Nausicaa is darker and more serious than the other ones here, but it's a must see. This one has a number of clear didactic messages that I won't spoil for anyone who hasn't seen it. You can later show it to any of your friends that scorn your passion for anime to help justify your hobby too.