You don't see it very often because they're careful with their feet. The tiny little tips of a spider's legs are oily. That keeps them from getting trapped on the sticky silk. The same thing happened with your fingers. Not all spiders use silken webs to trap insects.
Some spiders jump and pounce.
Others run after their prey and catch it. The shape we think of first for spiderwebs. You'll probably find lots that look like this. Tangle Web Lots of house spiders make this kind of web. The poisonous Black Widow does too.