I voted for all the option, except the last one. My preference? Anything with runny yolks.
The only one I didn’t select is raw. Besides that I like eggs in almost every fashion. I like runny yolks when I go out to eat, and I like nice hard ones at home that the cheese can melt on. I haven’t had at least two types in your poll, but I checked them anyway, because I think I’ll like them, too.
I was a bit unsure of some of the US terminology, but voted anyway.
You missed out pickled, and “boiled with a runny yolk, in an eggcup, with soldiers” 
Yes I do. Any style. I’ll crack a couple of eggs into a microwave safe bowl and cook them that way. I also have a gadget that hard boils them (safely) in the microwave.
Middle Eastern style: Fried until firm in olive oil, lightly salted, and then smothered in natural yogurt with lots of freshly-ground pepper. Serve with warm pita bread.
Over hard with the yolk broken is my go too. I also eat Sunny side cooked medium (no runniness and firm yolk but dipable with toast), hard boiled, Scrambled…actually I just really like eggs.
Mmmmm pickled eggs. I’ve had just straight pickled, pickled with jalapeños, pickled with garlic, and a few other varieties.
ETA: also left out are all the various species that lay eggs. Duck, goose, quail, chicken, fish, etc.
Now that I’ve looked it up, I’ll add “Shirred in a basket” too.
Mmmmmm, eggs.
But you left off powdered. When I was having breakfast on an airplane as a kid, I said I liked the eggs, and asked my dad if he was going to eat his. He replied “you would love breakfast in the military”.
Mmmmm, institutional eggs. Consistent consistency eggs.
I love eggs. My go to method is basted. Sparingly oil a hot, non-stick pan, crack an egg into it and let the bottom set up while you salt and pepper. Then hit it with a few tablespoons of water and throw on a lid. The key is to still have a runny yoke but with a thin cooked white top.
I’m an American and don’t really eat eggs that way, but when I hear “soft boiled” I picture egg cups and soldiers.
Huevos rancheros.
Coddled eggs with sharp cheddar.
I like over medium, with a slice of melted cheese on an English muffin or between two pieces of toast so that when you cut/bite into it, the yolk is a little runny but doesn’t get all over the place. Like a molten core.
Other favorites: deviled, scrambled, egg salad.
No options for custard?
This is the conversation I imagine Forrest Gump would have with his war buddy if they had planned on going into the egg farming business.
No love for thousand-year egg?
For breakfast, Eggs Benedict with lemon Hollandaise is my favorite. Followed by Over Easy/Medium, Sunny Side Up, Soft Scrambled, Omelet, and Quiche. For eggs anytime, it’s Egg Salad and Deviled Eggs.
Platypus, echidnas, alligators, pythons…
Like them most ways, but prefer runny yolks. Basted easy is probably my favorite, but scrambled soft are good, too. As are poached, omlettesl, even hard boiled are OK.
It’s nice to have something to sop up the runny yolk with-- toast or potatoes or pancakes.
Close. Over easy on TOP of the hashbrowns.