I don’t have many recipes that require only an egg yolk, but I have dozens that call for egg whites only. Since I don’t like to be wasteful, I generally keep pasteurized egg whites on hand for that purpose. (Supposedly you can freeze the egg yolks in an ice cube tray and then bag when frozen, but that just reads science experiment gone wrong to me.)
The other night I needed an egg white and didn’t have my handy carton available. Nothing to do but sacrifice a whole egg and then decide which method I wanted to use to perform the operation. There are several:
Old School Egg Separating Method
This one is super simple. I just crack the egg against the side of a bowl and use my thumbs to gently pull the egg apart, making sure the yolk stays in one side of the shell and allowing the white to spill into the bowl.
Swirl/slightly tilt the yolk side of the egg to push any remaining white up and over.
You can also pour the yolk from one shell half to the other, each time allowing any leftover white to spill out.
So simple.
The Professionals on Food Network Method
Another method I’ve used before is to crack the egg into my (clean) open palm and let the egg white spill between my fingers into the bowl. (I’ve seen the professionals do that on Food Network before, and it looks so…professional!)
The only problem with this method is that you have to stop to wash your hands, both before AND after. Bacteria, you know. (Not that I’ve ever seen the professionals wash their hands after doing it.
The Egg Separator Gadget in My Drawer Method
With this thing, you put the egg in the holder and the white drips into the bowl via slots in the bottom of the gadget. Not messy, but then you have a gadget to wash.
The Funnel Method
I haven’t done this one before, but I’ve heard that if you pour an egg into a funnel, the yolk will remain in the wide part while the white drains out the narrow part. It might be worth a try, especially if you’re separating lots of yolks and whites.
The This-Might-Be-Interesting-AND-Fun Method
It’s a short video, in which a woman uses a water bottle to “siphon” an egg yolk away from the white. This would be super handy for those times when a yolk escapes the safety of the shell half and slips into the bowl. Usually I just slip a fork under it and lift it out, but this would be way more fun. 
Those are the methods of which I’m aware. If YOU have other egg separating methods, I’d love to know them!