A doorstop often is an afterthought when calling out and installing the door hardware. The hinges (hang the door), the lockset/exit device (secure the door), and the closer (control the door) receive the most attention. The doorstop is an important component that keeps the other hardware functioning properly. A doorstop keeps other door hardware from damaging walls, bumping into & damaging other hardware, and preventing hardware from going past design limits & becoming damaged.
There are several kinds of door stops: spring, hinge pin, wall, floor, overhead, closer arms, kick down, and roller.
In residential settings, you'll usually find these three:

The most used doorstop is a spring doorstop. It's used when the door is free to swing against a wall. A spring stop is typically placed on the baseboard near the leading edge of the door.

Hinge pin doorstops should be used when there is not a wall for the door to swing up to.

Door Saver stops replace the hinge pin and control the door at the hinge itself rather than the door or frame. This prevents damage to the door, frame, or wall. While it costs more, it allows for a modern, clean, and minimal look.
Doorstops are just one component of a full hardware set. See How to Design a Hardware Set to learn more.
If you are interested in commercial door stops, check out our guide.