Mine was spirited away as well! I watched it with my cousins when I was visiting. I remember some parts terrified me as a kid, but I fell in love with it.
When I was about 8 or 9, I rented Princess Mononoke from Blockbuster by accident (they gave us the wrong movie), and fell in love. But I had no idea what the movie was called at the time, and this was the days before the Interwebs were as ubiquitous as today. I spent years trying to track it down. Finally, when I was in seventh grade, they got a new shelf of manga and anime graphic novels in, and there it was on. Remains to this day one of my favourite movies of all time.
Howls Moving Castle was my first, but Spirited Away is hands down my favorite. Grave of The Fireflies was also ridiculously good, even if a tear-jerker.