It’s so hard for me to get an egg cooked just the way I like it. In fact, I have a hard time making my own just right. But for me, the perfect egg is fried about halfway between over medium and over medium-well.
What about you?
Unfertilized.
And sure as night follows day, this response was going to be the first one after the OP. There was no way to stop it. <sigh>
I like mine over easy, as I like the yolk runny but not the white bit. I get quite bummed if the yolk breaks when I flip the egg.
OK, sorry for my predictability.
My favourite is poached. But it has to be done properly (no poaching machine for me, I like 'em freeform with a dash of vinegar).
Love eggs all kinds of ways. Once over lightly, hard-boiled, soft-boiled, stuffed in different ways, you name it. But if I had to pick an absolute favorite, I’d go for scrambled – the trick there is not drying them out too much when you cook them. Give them a good whipping (some people use a touch of milk, I don’t), cook them in a lot of butter, stir almost constantly and turn off the fire for the last minute or so – the heat in the pan is enough to finish the job and this allows you to get them just right. Not runny, but soft and fluffly. Yum.
For sheer decandence, substitute bacon drippings for the butter in above process. May not be great for your arteries, but it does wonders for your palate.
Hmm…I’ve just made myself hungry 
mmm eggs… I like mine scrambled, or absolute best ham and cheese omelette with toast.
Fried without oil, cooked so the yolk gently oozes.
Poached so the white has the consistency of crepe paper. No vinegar, please.
Scrambled, but differently to RedFury: lightly beaten and cooked gently with little stirring so the curds are not homogenous. Finished with a tiny dab of butter, sea salt, pepper, chives and parsley.
Hmm…
I usually poach my eggs. I have a little doodad I crack the eggs into, add a teaspoon of water to each egg then whack it in the microwave for 1m45s on medium… perfect!
If I’m feeling extra energetic, I’ll fry 'em… firm white but still runny yolk.
Otherwise I scramble them… mix in some cheese, salt, pepper, and cook it all until it just sets, then break it all up and add more cheese and maybe some mushrooms too… mmmmmmmmmmmmmmmmmm
runs to the kitchen
Max 
Sunny side up, with both the yolk runny and the while slightly runny.
over medium
I prefer mine over hard. I can’t stand for the egg to be runny.
basted or over easy, just enough so the albumen is not runny, but the yolk still is. Especially good on a bed of hashed browned potatoes.
Over easy with real hash browns.
Do you put ketchup on your hash browns?
Scrambled. And smooshed onto toast.
With a side of hash browns (no ketchup)
And orange juice. Small.
I eat 'em every which way. It changes with my mood.
When I fry them, I like to toss a half-tsp of water into the pan, and then cover it…after about sixty seconds, the steam cooks the tops and you end up with a perfect cross between sunny-side-up and over-easy.
But always with sausages, potatoes (no ketchup, thank you), buttered rye toast, and a cold V-8, lemon on the side.
Never. Although I do crack when I go into a Waffle House and the waitress hollers out “I need hashbrowns cuffed, stuffed and muffed and fluffed”. Okay that may not be the exact terminology but it is funny nonetheless.
Eggs - the versatile food. They are yummy in most ways - deviled, scrambled with just a tad pepper (other ingredients make it a messed up omelette), hard boiled, fried with just a smidge of runny yolk (a bit like yours Lib), or poached with the yolk nearly cooked through.
I cannot stand runny yolks. Just disgusting. However, if the yolk is still a bit soft and spreadable, all the better.
It is hard to cook just the right egg, even for yourself, at the best of times. In a restaurant it is even harder. Much easier to ask for a dead egg then risk gooeyness.
Hashbrowns, crispy with a dribble of ketsup and generous dashings of Tabasco.
No ketchup, but a nice dose of Louisiana hot sauce.
Exactly. If the egg isn’t underwater, it’s not poached, and a poached egg on English muffin is a real treat.
Though usually, I have them scrambled. If I’m feeling decadent, I make it with heavy cream or add cheese, but the usual recipe is to scramble the eggs and milk, add some fresh-ground pepper. and cook them until they no longer glisten (no longer – otherwise they’re too dry).