I am always on the lookout for beautiful, simple films that children and adults can enjoy together. These tend to be quiet films, with a strong story and strong characters, and plenty of visual interest. My adoration of film comes partly from my upbringing and partly from my college studies.
I stumbled on this delightful stop-motion film by Tsuneo Goda when I was investigating the origins of Domo. (the original Domo Japanese ads, also stop-motions by Goda, are also worth seeking.) A True Friend is broken into parts on Youtube. I watched it in these parts with Lulu for bedtime a while back, and we both found it highly enjoyable. There is little dialogue and the soundtrack is sparse--it's a quiet film, which helps to draw the viewer into the magical world Goda has created.
I have posted all four parts here. I recommend showing it in parts and discussing each part with your child as you watch. Watching films at home with children is ideal--you're in a familiar, controlled setting, and you have control over the film. Stopping for discussion or to take breaks during a long film should be part of the process for a young viewer.
This film is suitable for ages 3 up. If you watch tv/films with your two-year-old, this one should be fine once you get past the first Yeti sightings. Of course, I recommend you preview it and any film first since you know your child best.