Studio Ghibli (Headed by Hayao Miyazaki) produced some of the best and most memorable animated films. Movies ranging from light hearted ("My Neighbor Totoro") to serious ("Grave of the Fireflies") have been released and generally received a lot of acclaim. I have not seen 2004's Howl's Moving Castle, so this list will probably be updated after I watch it.
Like "My Neighbor Totoro", this movie is produced with younger audience in mind, however, I found this movie to be highly enjoyable for adults too.
See the full review, "Cute and enjoyable for all ages".