What exactly is the purpose of hub centering rings? What can be the result of not using hub centering rings? It looks like with a 5 lug hub that the rings would not be needed....

Its a ring that snaps into the back of the wheels center bore hole. It ensures the wheel doesn't sag on the hub when bolting the wheel down. This way, its not bolted down crooked which causes the wheel to vibrate. Instead of using the lugs and studs to center the wheel (bad bad bad) the ring does it.

Also, many wheels will be made in one fitment with one hole size. Example, an 18x8 with a 5-100 bolt pattern. Well, that fits many many cars but the hub hole might not be the same on each car. In steps the centering ring to change the hub size so the wheel will fit many other cars. This way only one wheel with many fitment possibilities can be made instead of one wheel for each car. That would cost a lot!! Around 90% of aftermarket wheels use a hub ring.

Don't confuse it with a spacer that fits between the hub and wheel or that changes bolt pattern. See pic for example of a ring.

Thanks for the info.

What could be the probable result of not using hub rings? Could it cause the wheel to come loose, or worse, come off the car?

Instead of the wheel being centered on the hub, its rests on the studs when bolted down. When driven on un-centered you can get a bad vibration. If severe enough, you can round out the lug holes, seats, and even hub of the wheel. Its a pretty important part.