Some people like their fried eggs cooked so that the whites get absolutely no color. You can count me out of that crowd. What's the point? Why not just poach your eggs and call it a day if that's what you want?
No. When I get fried eggs, I want them to taste fried. Frazzled, brown, crisp-edged, the yolk still runny; is there any delight greater than dipping the edge of a crisply browned egg white into an oozy golden yolk?
For my money, there are two cultures that cook eggs better than any other in the world: the Spanish and the Thai. Both rely on the same method, and it's simple: break an egg into a good amount of very hot fat. That's it.
Ok, that's not quite it. If you want to get extra fancy, you can spoon said hot fat over the top of the eggs as they cook, causing them to bubble and blister on their surface and helping you rapidly achieve crisp-whited, soft-yolked nirvana.
Once you've got the egg down right, it's just a matter of what to serve it with.
Going the Spanish route, chorizo seems like an obvious choice, and I can't think of a better medium for frying eggs than a good mixture of rendered chorizo fat and extra-virgin olive oil (this also gets you the advantage of crisp chorizo bits with which to garnish your meal). Adding a nice green vegetable like asparagus will turn breakfast into lunch or a light dinner, and a good ol' smear of allioli (the Spanish version of Provençal aïoli) flavored with smoked paprika will turn a light dinner into a full-on meal that can be prepared in just about 15 minutes.
Just make sure to have some good bread on the side—there are too many dippable items on this one plate to even mention by name.