"Yes, cobwebs are made by spiders. Arachnologically speaking, a "cobweb" is a web made up of short irregular strands arranged haphazardly, as opposed to the elegant and elaborate orb webs made by spiders of the family Araneidae. The "cobweb spiders" make up the family Theridiidae. One of the commonest in the U.S. is the common house spider Achaearanea tepidariorum. Because the strands are sticky, they gather dust, producing the long fluffy streamers you see. The notorious black widow spider Latrodectus mactans also belongs to this family. Another spider which may be responsible for webs around the house is the long-legged cellar spider Pholcus phalangioides of the family Pholcidae, which makes loose irregular webs in dark places.
Some stray strands of cobweb aren't (and never were) part of a web, haphazard or otherwise, but are produced by spiders or other arthropods just the same. Jumping spiders, for example, trail a dragline wherever they go, but don't make webs. A single filament like this can sometimes get into the airstream and land and stick somewhere. Likewise, as readers of Charlotte's Web know, many spiders will disperse from their egg sac by "ballooning," which involves trailing a long filament of silk from the spinnerets until the air currents catch hold (like flying a kite more than ballooning, I suppose). These filaments can obviously occur indoors if that's where the egg sac was located, or they may blow in from the outside. Similarly, many tree-feeding moth larvae will make silk "escape" lines if they feel threatened, and these lines can break loose and get into the air.
While we're on the subject, you're probably wondering what a "cob" is. Here's what the Word Detective says:
The most commonly encountered "cob" is the corn-cob, the cylindrical woody shoot on which grains of corn grow. That kind of "cob" comes from a very old English word that meant "head or top."
It is possible that "cobweb" is related to that word, but a more certain ancestor is the Middle English "coppe," which meant simply "spider." Over the years "coppe" was gradually slurred to "cob," and, voila, "cobweb." "
— George, Doug, and Ken
www.straightdope.com
