Statues of fictional TV characters is an interesting thread, but how about statues for real-life people or animals that are a bit odd?
I will start: Fort Benton, MT has a statue honoring Shep, a real-life sheep dog. One day his owner boarded the train and did not return. The sheepherder had died. Shep faithfully came to meet every train for five years, hoping his master would come home. One day Shep slipped on the ice and was killed by a freight train. The townspeople buried him on a hill outside of town and there is a statue of ole Shep - a model of canine fidelity.