Evolution of spider webs?
I kind of hate using Wikipedia as a reference, but this article offers a general overview of spider evolution...
https://en.wikipedia.org/wiki/Evolution_of_spiders

And this article mentions fungus gnats (and perhaps other species) as examples of convergent evolution...
http://www.mapoflife.org/topics/topic_267_Silk-production-and-use-in-arthropods/

I can't remember with certainty, but I believe some jellyfish (and/or perhaps other marine invertebrates) have sticky tentacles that function somewhat similar to spider webs. In fact, some carnivorous plants have sticky structures that trap prey.