Another spidery fact and how my colleagues found out I'm scared of spiders.
Spiders have an exoskeleton made of chitin which is flexible enough to allow them to move but like our own hair and fingernails is 'dead'. This means for the spider to grow it must shed the old skeleton (warning spider images, I had to get my wife to find the link!) and grow into a new one. Most of the time you wouldn't be able to find the old skin unless the spider is big...
I had this fact brought home to me one sunny day at a hospital I used to work at. I was chatting to the receptionist when the head nurse walked in with a plastic box. She opened the box and thinking she was offering cake I looked eagerly in. I think they were both a bit shocked when I ran screaming into the car park. The box actually contained the shed skin of her son's tarantula which she thought we might be interested to see. She was very apologetic and I was very embarrassed !
I wasn't able to search for images of 'exoskeleton' as I know what will come up, but here is a clue to two other creatures that have exoskeletons.