With onions, peppers, sausage, lots of cheese, anything to convince me it isn’t just eggs.
In order of preference:
- Over-easy (dipping the toast in the yolk)
- Scrambled
- Over-hard (served with toast in an egg-and-cheese sandwich)
- Omelet – if I have interesting ingredients to use (mushrooms, broccoli, cheese, bacon…)
I like 'em over medium. That way you can dip 'em, but the yolk is kinda sluggish and doesn’t escape all over your plate.
My kids learned to fix eggs in a blanket at camp: tear a hole in a slice of bread, crack an egg into it, fry in butter on both sides. MMMM! Built-in toast!
I am split evenly between fried hard with the yolk broken and a nice omelet. Either one could be with or without cheese.
Depends, but I’m ashamed to say usually over-hard, with leathery-crunchy bits. Sometimes over medium if I plan to put it on top of something absorbent, like an english muffin or a pancake.
My favorite way to fix them would probably be fried over easy (closer to over medium, but that wasn’t an option).
My favorite way to have someone else fix them is poached, but I never want to go through the trouble for myself.
I like over easy if I’m topping something with them: hash, beans, fried taters, biscuits & gravy, etc. We usually have scrambled in the morning, which I like with herbs and a glob of cream cheese mixed in at the end.
I like then any old way, but my favorite is to make a hole in the middle of a piece of bread, and saute’ it in butter with an egg in the middle.
When I was a kid, whenever I wasn’t feeling well, my mother would fix me soft-boiled eggs. It’s still one of my very favorite ways. You have to eat them properly, though: soft-boil the eggs, wait until they’re just cool enough to handle. Put a little pat of butter in the bottom of a bowl, scoop the eggs out of the shells onto the butter. Add salt and pepper. Crumble in saltine crackers until just the right consistency is reached. If you don’t know what ‘just the right consistency’ is, obviously you don’t deserve soft-boiled eggs! 
BTW, if you really want to keep your scrambled eggs moist, do the low-and-slow method for cooking, but also add a couple of playing-dice-sized cubes of cream cheese to the eggs. Mmmm. Moist, creamy, silky, perfect with just a dash of dried herbs, salt and pepper!
I would call that scrambled eggs with bits in them. I don’t call it an omelette unless the cooked egg forms a layer enclosing a pocket of fillings.
When I was little, we called these “Eggs in a cage”. Very good, and I’ve never met a kid who didn’t like them!
I’m too lazy a cook to even bother dirtying an extra bowl for a proper scramble. So I just sort of scramble them in the pan. More of a fried over hard, I guess, so that’s what I voted.
Crack directly into oiled pan
Salt & Pepper
Break yolks with edge of spatula and smear around.
Let cook a bit
Flip
Let cook a bit more - add cheese at this point if I feel like cheese
Slide out of pan and eat
Really just the laziest possible way to do it.
Another one for over medium. I like 'em medium boiled, too, but over medium is they way. Didn’t vote.
You want to know what works really good in scrambled eggs? Green olives with pimentos.
It looks like scrambled is winning, and probably because people think it is the easiest or it is the only way they can make that seems to come out correctly =)
Nothing against scrambled, they are perfectly good, I make them myself - dash of assorted herbs, a teaspoon of milk per egg, and when plating some shredded cheddar and top with a couple grinds of fresh pepper. Sourdough toast, and 2 strips of bacon, it is mrAru’s favorite breakfast.
Omelets are not too much more difficult, and there are 2 types, the fluffy type and the very thin flat type. I prefer the fluffy type, everybody else in my family when I was growing up [referred the flat type.
My true love is poached, or soft boiled with the yolk nice and runny so it soaks into toast. A lovely variant of this is coddled. Eggs florentine is amazing, left over rice mixed with chopped frozen thawed and squeezed dry spinach with a touch of cream and butter in a ramekin, make a well in the top and crack an egg into it, top with a dab of butter and a large pinch of parmesan cheese, some italian herbs and pop it into the oven at about 300 until the egg is set as firmly as you like it [runny or solid] and enjoy with a mimosa <nomnomnom!> or a southwestern variant, black beans mixed with salsa, egg in the top, more salsa and queso fresca …
Isn’t it amazing how versatile the basic egg is?
Zabaione does it for me, every time. If it’s just plain breakfast eggs, I like them either boiled for six minutes (the yolk shouldn’t be runny or crumbly but dark yellow and slightly creamy), or softly scrambled.
Hard scrambled. I mean, to the point where there are browned sections. Absolutely no runniness at all. It’s the only way I’ll eat eggs (other than, “hey, try XXX that I made”, 'cause I’m not rude).
Fried over-easy. It’s also my favorite way to eat them. I can’t flip them with just my pan, but I have developed some mean spatula skills! It’s funny when my SO tries to make eggs for me. He always tries to cook them too long.
Me: They’re done now.
Him: But I JUST flipped them, like, 5 seconds ago!
Me: I know! They’re done! Gimme!
I can’t eat runny whites, but as long as they’re just barely cooked I consider my eggs done 
The second-best part about over-easy is they’re done quickly and I get to eat breakfast sooner. The best part, of course, is the runny yolk.
Eggs are very hard to fix. Better not to break them in the first place.