I think the egg is one of the most amazing foods in existence. Incredibly versatile, incredibly tasty, and absolutely brimming with nutrients that are hard to find elsewhere (choline, anyone?), they can also be an excellent convenience food.
Allow me to pimp a product for a minute, because it has improved my already good relationship with the egg http://www.amazon.com/gp/product/B0007M2BN0. This little gizmo, which cooks eggs in the microwave, is a LIFESAVER in the morning.
I'm a huge fan of soft boiled eggs for breakfast. I also love hardboiled eggs minced up on salad, and a frittata is a great way to deal with leftovers.
I look back on my egg white eating days with some amusement. I never really liked egg whites on their own, but I made myself eat them for the protein. Not that they were all bad, especially topped with a slice of cheese.
But the lovely, luscious soft yolk is definitely the best part. I will never forget my first salade Lyonnaise--frisee, bacon, and poached egg perched on top, pierced so that it would run down the leaves of the frisee and mix with the bacon grease, forming a totally delicious dressing.
I even eat eggs raw (gasp! scandal! salmonella!) mixed into steak tartare or in homemade caesar salad dressing. Each cooking method, or lack thereof, brings out something different in the egg.
The only thing you HAVE to do with the egg is handle it gently. The proteins in the egg do not react well to high, dry, heat--they seize and get tough and become, in the words of one great french chef "elephant skin." And anyone who's had an overcooked hardboiled egg can attest to the tongue desiccating nature of overcooked yolk. But treat the egg with love and patience, and it will repay you handsomely.
I'll finish with a cooking recommendation, rather than a recipe, because this is more technique than anything. For a truly indulgent, glorious example of what the egg can do, I recommend scrambling two or three gently in some clarified butter, over low heat. Stir the eggs gently and slowly in a figure of eight motion until just barely cooked through. It feels like eating rich, creamy, yellow clouds and it is possibly my favourite meal on a Sunday morning.