Anything by Studio Ghibli is made of Awesome. Spirited Away, Howl's Moving Castle, and My Neighbor Totoro are the best. There was nothing wrong with Princess Mononoke in my opinion. The Cat Returns and Kiki's Delivery Service are probably more geared towards younger audiences, but they are highly enjoyable. If you're into mindflock animes, FLCL and Ghost in the Shell (either the original, Innocence, Solid State Society, or Stand Alone Complex 1/2) will do, as well as Ergo Proxy.