Sounds like Korea and America are mostly(?) the same -- fried eggs, boiled eggs, scrambled eggs.
A really good question would be 1) What do you put *in* your eggs, or 2) When is an egg "cooked"?
I remember my Swedish friends loved eating soft-boiled eggs....that is, they would stick an egg in boiling water for all of a minute, so that the white would solidify, and eat the soupy yolk. To me, that's just... it's not done. It's raw. And yet I do the same thing with my fried eggs - cooked white, nearly raw yolk. Though I prefer "over-easy" - flip the fried egg over once before serving, so that the thin layer covering the yolk also cooks.
My ex, on the other hand, claimed that if you didn't cook the yolk until it was completely solid, you would die of poisoning or some such.
Here in Japan, while people certainly love their fried eggs and omelettes, it's much more common to find egg rolls. You add soy sauce, cooking alcohol, and sugar to (one/a few) eggs, mix, and cook in a special square pan. As it starts to solidify, you very carefully roll it up into a log, and then slice to serve. Raw egg yolks are also a common (and delicious!) addition to rice or beef bowls.
In my hometown of Western Pennsylvania (US), a great local snack is pickled eggs. You hard-boil some eggs and shell them, then pickle them in a mixture of vinegar, sugar, black pepper, and pickled beets. Leave them for about 3 days until they turn a delightful shade of magenta, and then chow down!