I want to point out that I don’t really use a lot of screws in woodworking. Usually I use wood glue, which is stronger and leaves no visible fasteners. The downsides to glue are that you have to wait for it to dry and once you’ve assembled something, you can’t take it apart.
I often use screws for shop projects and jigs. With these, I’m not concerned about the appearance as much and love the time-savings screws give me.
Screws are also used to hold things together where expansion and contraction of the wood can be an issue. A common use is to attach a tabletop to a base. The screws will be set into a slot, allowing the wood to move as humidity changes.
For some projects that are sort of in the middle ground between making an heirloom dresser and a workbench, I like to use pocket screws. They are great for making cabinets and other casework. They make assembling these types of projects, say a bedframe, much easier and quicker. And of course, you want to position the pocket holes on the undersides or back of projects where they won’t be visible.