What is the most famous example of biomimetics?

Probably, the most famous example of biomimetics is Velcro.

In 1948, the Swiss engineer George de Mestral was cleaning his dog of burrs picked up on a walk,instead of being annoyed, he had a further look at things under his microscope.

He then realized how the hooks of the burrs clung to the fur. This gave him the idea to recreate the some mechanism artificially, thus we have Velcro.