Well, it depends upon how you define vegetable and how you define favorite. In Mexico, corn is a twice daily necessity, to eat with tortillas, which are practically a table utensil. In the States, wheat is what makes bread and pasta, also a daily foodstuff. Rice and potatoes as well, are everywhere. I start nearly all of my cooking with onions and garlic. So by the old-fashioned definition of vegetable — videlicet, Kingdom Plantae, it grows in the ground — those would be the biggies.
But if we eliminate grains, roots, tubers, and nuts, then I guess the tomato. Though technically that’s a fruit. Hmmmmm. Carrots and celery? Great on their own, the mirepoix to start all good sauces, braises, soups and stews, and a nice finely minced addition to tuna salad, egg salad, potato salad, etc. I like very small petit-pois also.