How Many Creatures Don't Have a Brain?

Some creatures that don't seem to have a brain at all are capable of amazing feats of building. Look at a spider web. They not only produce their own webbing, but I was listening to a video the other day when a spider builds. Some of the spiders actually leave one wedge of the web without any crisscrosses in it so that they can zoom down this non-sticky part and get to what they want. And just how does all that happen? Right. Like with a caterpillar that just wanders around eating a lot of stuff and then it dissolves into a goo once it gets inside the chrysalis - there's no brain or anything left.