The bur of the burdock plant's fruit kept getting stuck on a Swiss engineer's clothes, so he eventually created the hook system called velcro
The bumps on the Stenocara beetle hold water extremely well, and people have started using it in nets to capture water from the air.
A slime mould grew in the most efficient network, and Japan noticed this and used it to build its train system.
Mosquito proboscis inspired a less painful needle.