It depends on the ethnicity of the egg dish.
For a traditional American egg dish, I vote for the Western omelette, Denver omelette, or the basic ham and cheese omelette. A typical American egg breakfast you can't beat is two eggs over easy or scrambled, 4 slices of bacon, and hash brown potatoes, with toasted bread with butter and fruit preserves or pancakes with syrup.
In the southern United States, biscuits with sausage gravy, ham steak with red-eye gravy, or chicken fried steak, along with eggs any style and grits is customary and I do not shy away from it.
For Mexican, it is definitely huevos rancheros, or huevos y chorizo if I am in a hurry.
For Italian, I will always love a traditional fritatta, traditional meaning with diced potatoes, meat and cheese. You can add peppers and onions if you wish, but say nay nay to milk, cream or flour (that would make it a soufflé). Runner up to the fritatta is uova del diavolo, a.k.a. eggs in purgatory.
From Spain, I like a Tortilla Española , which is absolutely nothing like a Tortilla Mexicana, but is similar to an Italian Fritatta, with only potatoes and onions. I have been known to serve Mexican tortillas along side a Spanish tortilla.
I will pass on British bangers and mash or Irish bangers and colcannon.
