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).
A Gracious Tone. Your resignation letter is not the time to air grudges, take passive_aggressive shots, or otherwise be unpleasant. Regardless of how you feel about your (soon to be former) job or your boss, this letter should be an exercise in professionalism and graciousness. An excellent way to do that is to say a simple "thank you." Even if you hated your job, you got something from it at some point. Focus on that positive bit if you need to.