Myth: Spiders have oil on their feet that keeps them from sticking to their own webs.
Fact: Everyone who educates about spiders has heard the question "why don't spiders stick to their own webs?" many times. Who first came up with the oil-on-the-feet idea is unknown, but it must have originally been a perfectly reasonable guess, or hypothesis. Since the decades-old origin of this idea, in some circles it's become a dogma. It's been repeated countless times in print and online. There are even classroom lesson plans built around this false "fact".
To quote two of the world's leading experts on spider silk use (Fritz Vollrath and Edward Tillinghast) writing in 1992: "Ecribellate spiders simply tiptoe around the glue, which they deposit in spheroidal globs. When a spider accidentally steps into one of these glue balls, as it sometimes does, it suffers no more inconvenience than a human stepping into a wad of gum. When a fly slams into the web, however, it hits about 50 of the droplets, enough to make it stick." I might add that 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.
To clinch the matter, investigators have found no oil-secreting glands opening on spider tarsi (end segments of legs). 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.
The very latest word on this topic is a 2012 study by R. Briceño and W.G. Eberhard. They found there is one time when an orbweaver does contact its glue drops, hundreds of times, and that is when making the web in the first place. The parts of the tarsi used for this are covered with special branched hairs that keep the glue from touching the leg surface. There may indeed be a chemical involved (not identified yet, probably not an oil).
I'm indebted to Ohio University arachnologist Jerome Rovner for the germ of this article.