Nausicaa of the Valley of the Wind, though it's technically not a Studio Ghibli film since it was made before the studio was formed. If that doesn't count, I think either Kiki's Delivery Service or Porco Rosso was my first one. I wasn't really hooked by either of those two though, although I've come to appreciate them now. Castle in the Sky and Princess Mononoke really won me over though. I'm not sure if I really understood them back then as a kid, but I remember being pretty amazed by the mystical wonder of the city of Laputa and the Forest Spirit in Mononoke.

I've got some catching up to do though. The most recent Ghibli film I've seen was Ponyo.