My son eats lots of what we eat, though he's recently (age 6) decided he doesn't like several foods he's enjoyed literally for years -- apricots and ravioli (usually some version on Trader Joe's, either spinach or cheese) spring to mind. Oh well.
Beans. He'll eat pretty much any kind of beans or peas -- black beans, black-eyed peas done in the crockpot are common parts of our meals. Sweet potatoes (he's not so much a fan of real potatoes, though if I roast up a pan of beets/carrots/potatoes I can give him mostly the carrots and sneak in a bit of the others around the edges). Green beans, broccoli, green peas, corn, brussel sprouts -- he will eat all these, I usually just buy frozen and cook in the microwave with a bit of butter. Raw carrots. Raw cherry tomatoes. Cheese quesadillas (I use whole wheat quesadillas). Eggs. Pretty much any meat we eat, and we do -- chicken, sausage (not spicy), pork, beef stew or steak, various fish, shrimp (obviously these may not be fast, depending how you cook them, but if you're making some anyway...) . Toast. Grapes, apples, berries, pears, bananas. Peanut butter sandwiches. Popcorn (I like to stove pop but will also use the not-too-doctored microwave stuff, he reports liking that better, though I'm doubtful he can really tell the difference if he doesn't see it cooked...). Spaghetti.
Gosh, reading that I see that my kid eats pretty much everything (except ravioli and apricots), so my experience may not be too relevant to you. Generally if he won't eat what I serve I offer him one other "easy" alternative, i.e. "you can have a sandwich instead" or "you can have a cheese quesadilla instead," but not a range of choices.