Ghibli

I recommend watching any film from the Japanese animation studio, Studio Ghibli. They are by turn funny, moving, compelling, and always beautifully made, with an incredible attention to detail.

This is roughly half of their feature film output. These DVDs are numbered by the distributor, rather than being in chronological order - I'm not sure why, but I'm guessing it may have to do with when they received the rights to sell them.

If you haven't seen any of these films, I'd suggest a great place to start would be either Kiki's Delivery Service or Princess Mononoke.

Please do try and see some of them if you can.