Spiders have oil on their feet that keeps them from sticking to their own webs.
Investigators have found no oil-secreting glands opening on spider tarsi (end segments of legs). Most spiders don't even make sticky silk, and those that do (mainly orbweavers and cobweb weavers) still have many non-sticky threads in various parts of their webs. One unique feature web-making spiders do have on their tarsi is a third claw opposable to certain specialized bristles, enabling them to grasp individual threads. No insect has more than two tarsal claws per leg, and most are helpless in a web.