Other recommendations: The Cat Returns (sorta funny), Grave of the Fireflies (very sad film), Kiki's Delivery Service (it's entertaining), My Neighbor Totoro (very cute), Porco Rosso (one of SG's few male-heroes, but entertaining nonetheless), and Tales from Earthsea (first watch Princess Mononoke, if you enjoyed that, you may enjoy this one).
The next Studio Ghibli films I have to see are Laputa: Castle in the Sky and the latest film Ponyo on a Cliff. I've been meaning to watch those two for awhile now.