Princess Mononoke was the first one I saw, and then in no particular order after it was Spirited Away, My Neighbor Totoro, Castle in the Sky, Nausicaä of the Valley of the Wind, Kiki's Delivery Service, and Howl's Moving Castle. Half of those I've only seen once because I never actually owned them, just rented. I definitely haven't been keeping up with any releases since HMC, and I certainly haven't watched all the older movies. I will eventually get around to watching them. Maybe.
Favorites are probably Princess Mononoke (for being the first I saw) and My Neighbor Totoro. Howl's is kind of up there as well, except it's a bit spoiled in my view by me having read the book and ending up thinking that the movie, while pretty, is only an "okay" adaptation.