We do very simple omelets. Our three most popular are western (green pepper, yellow onion, ham), diced turkey & hot salsa (drop the salsa by the half teaspoon onto the egg when it has just begun to set up), and the simplest; diced tomato & basil, with or without mozzarella.
I've found very few meats or whole ingredients that don't go well in omelets. Fruits are likely out (more of a crepe thing). Dunno about lettuces. Perhaps no citrus, unless a lemon-pepper chicken or pork. Beans might be nice. Hash browned potatoes, certainly. Fresh herb blends, like pesto, I would like. Hmmm, babaganoush omelet? Maybe not, but I'd probably try.