However, at most companies, there's no formal requirement that you do so. Most employment in the United States is called "at will", which means that your current employer can fire you at any time and for any reason (except those that are prohibited under law).
Your End Game. When you hand in your resignation, it can kick off a bit of chaos__your position will need to be filled, but your duties will also need to be covered until they can replace you. As part of your resignation letter, it's a good idea to convey what your availability is during that transitional period.