I would say anthing and everything by Hayao Miyazaki and Studio Ghibli
Here's a full list...
The Castle of Cagliostro, one of my favorites, stars Lupin the 3rd and has some of the most fun action ever.
Nausicaa of the Valley of Wind, the manga is better but the movie is still worth watching.
Castle in the Sky, pretty much every RPG rips off this movie and does it poorly.
My Neighbor Totoro, if this movie doesn't charm you... you have no soul.
Kiki's Delivery Service, it's like bottled happiness, though not quite as much as Totoro.
Porco Rosso, a movie about a WW1 flying ace in Italy who also happens to be a pig, my personal favorite Miyazaki film.
Princess Mononoke, probably Miyazaki's most mature and violent film and with one of the strongest stories he's ever told.
Spirited Away, probably Miyazaki's BEST film in terms of story, charm and animation.
Howls Moving Castle, Miyazaki's weakest film but still worth it for the cool scenes and machinery, even if the ending is extremely rushed.
The Cat Returns, a rousing, sugar coated adventure that will make you feel good.
Whisper of the Heart, a cute film set in the real world, a little slow, but like I said, cute.
EDIT: Yes I know I missed Grave of the Fireflies, that's because I haven't seen it yet, I don't know if I can handle that level of sadness.
