I almost never order an omelet in a restaurant. Too big, too fluffy (often watery), not browned properly and worst of all, cooked in rancid frankenoils. You can really taste it unless, of course, you get one of those kitchen sink omelets loaded with so many ingredients you can't properly taste any of them.
Oh, and don't forget the plastic cheese that even some upscale restaurants use. When I make omelets I generally stick with one ingredient. Often that's onion. Sometimes bacon. Rarely cheese. When I do onion it's what I call a "burnt onion omelet." Slice 'em thin and then let them sit in butter until nice and toasted brown/black, them pour in the egg & finish it off.
Another version is a simple brown butter omelet. Simply let your butter (lots) sit in the pan on low until the milk solids get really brown, then finish off your eggs.
That's what this one was, accompanied by bacon (click for the hi-res version).
Brown Butter Omelet
I believe this one was one of my rare late evening snacks. Used to do that a lot, but hardly ever do I eat anything after my dinner meal anymore.