Here's another classic Aardman animation. This actually might be my favorite of all their shorts, and the soundtrack has a fair bit to do with it. "Wat's Pig" (1996) is the story of twin brothers, separated as babies, and their diverging and converging lives. It's a great example of just how much in a story can be conveyed non-verbally. Only one word is used in the whole of it all.
Despite being the title character, you hardly see Wat's pet/mom pig at all. The split screen effect is creatively done too, and the sets are beautifully detailed. Claymation is so cool.