A short report in Science in 2006 described an 'Early Cretaceous Spider Web with Its Prey'. This was the worlds oldest preserved spider web. Preserved in a large blob of amber the web and the insects caught in it have now been dated to the early Cretaceous - about 110 million years ago.
Although the web is not complete enough for scientists to reconstruct it, enough remains to suggest this was not just a collection of strands and was probably in one plane like an orb web.
As you can imagine finding fossilized spider webs is unusual. We do know that fossilized spiders have had spinnerets for producing silk for closer to 400 million years.