Besides Aesthetics (Looks)?
Protection for the components from kids wanting to touch, cats wanting to touch, bugs, or physical damage like things dropping on it, liquid spills.
Dust protection/Dust Filters
Directed air flow. I mean, you could point a box fan at all the components, but case fans and cases are usually designed to manage heat in a way that goes beyond just removing heat from the case, but rather directing that cooling air across the motherboard as a whole and other components like RAM with their little heat sinks, etc.
Convenience such as front end headphone/mic jacks or easily accessible USB ports. You can tack on to that things like power button, reset button, or drive bays for something like a multi memory card reader or optical drives.
Portability. I mean, desktops range in size, and they usually aren't purchased for portability, but having it all in a case usually means you can throw it in the back seat of a car for a move, for an event, or whatever.