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).
You'll have plenty of time to vent personally about your work grievances as you leave, but really, you stand to gain nothing by putting negativity into your resignation letter. And unless you're leaving the state and your current industry, you always run the risk of running into the same people later on. So you're far better off taking the high road and making sure your exit is a classy one.