Over-hard eggs are like well-done steaks, they are an abomination and cannot be called ‘food’.
I like my yolk runny and the white set.
Served on toast. Cut it up and enjoy.
Occasionally I’ll fix grits. Love my eggs on grits. Cutting the runny egg and getting a scoop of grits too.
I eat them two ways. Sometime is will fry them hard, very well done with melted cheese on top and eat it with a fork (and salt and pepper).
The other way is Sunny-side. I like the white cooked through and soft yolks. I eat those with toast or bread for dipping.
With salt.
Yes! They’re even better, if you mix grits and patty sausage into them.
And now I want fried eggs.
With black pepper and sometimes hot sauce.
Sunnyside up - I cut the white away from the yolk, then take a piece of white bread and eat the yolk by sopping it up. When the gooey part is gone I put the remainder on a piece of bread, put some white on it, and put some bacon on that, and munch it down. Repeat for each egg I cook, usually two.
Oh, and I take any remaining bread to soak up the butter left in the pan I cooked the eggs in.
Fried hard (because goopy eggs are blechhhhhhhh), as a sandwich on toast with butter, a little mayo, and a slice of cheese.
Semi-hard, just straight across in bites, especially when it’s between two slices of bread with a little mayo.
Over easy to medium, bust the yolk and dab at it with toast while eating the whites. Prefer a little diced jalapeno in the pan before busting the egg in. If I break the yolk, as above.
Often in sandwiches, with cheese and bacon or ham. I don’t mind if the yolk is a little runny. Also with grits, either mixed together or separate. Toast is good for sopping up runny yolk.
I prefer to cut the white away from the yolk and cut it into pieces; then scoop up the intact yolk and eat it whole. This way I don’t lose any yolk liquid. Once over medium. 
Also, a friend of mine used to make fried-egg-and-bacon sandwiches for herself and me. Really good. What’s strange is that she is from a Jewish family (her parents didn’t keep kosher, either).
If any of the yolk has firmed, the egg is ruined. I try to get a little yolk and white in each bite, with plenty of yolk left to sop up with toast.
I took the poll option that says “mix it all up” but that’s not quite exactly right.
The first cut should go from the perimeter of the egg white into the center of the yolk, allowing runny yolk to spread into the cut and make sure that your first bites have some yolk on them. Once about half the egg white has been eaten, just make sure to cut each bite to include a little yolk and a little egg.
As for firmness of the yolk: when I was young, I hated runny eggs and even broke the yolk while cooking to ensure it was fully cooked. I can’t remember what age started my transformation into proper egg eating, but I think it was during my high school years. Today, my technique is sunny side up, but cooked with a lid over it to make sure the top steams thoroughly. The pan temperature is high enough to get crispy edges around the white even covered.
First, season over-easy eggs with a little salt and a lot of pepper.
Second, break the film on the yolk with buttered toast and take a bite of the yolk-soaked toast. The breaking-of-the-yolk can also be done with bacon or link sausage.
Third, mix eggs with hash brown or home fries. Yum!
Alternatively, if serving your eggs with pancakes, waffles, or french toast, place the egg on top, break the yolk, allow it to soak into the pancakes, then pour syrup over everything. Also yum!
I just place my mouth over the yolk, and then slurp.
Hard.
Unless it’s in a sandwich, I’ll open it on a piece of toast–toast soaked with hot yolk is nicer than scrubbing yolk up off the plate–then cut it into bitesized pieces from the outer whitey bits, working toward the center.
I vote for this.
If they’re on the plate, along with sausages/bacon/ham and toast, I eat about 50% of the white speared up with meat and a bite of toast, then cut into the edge of the yolk and let it ooze out onto the plate. The following bites of egg, meat, and toast are garnished with the delicious, delicious yolk.
Once in a while I will fry an egg and set it upon one half of a slice of soft white bread, then fold the bread over it and lift it in my hands to eat sandwich style. The aim here is to nibble the sandwich down, bite into the yolk, then get some yolk in every bite without letting the yolk dribble down over the fingers.
I’ve told my children this is like having a delicious breakfast and an exciting game all at the same time.
I am glad to see that a few of us are intelligent enough to fry our eggs until they are DONE. Runny yolk is an abomination and runny white has been known to make me throw up in my mouth and not a little. I break the yoke with a fork so that there is no bare white glaring at me and cook the egg (in butter, naturally) until cooked hard. When I was a kid my gramma would fry eggs for the family and she always made me wait until she broke a yolk. Which she never did. So I got my egg last. Sigh.