Americans do tend to be more informal than people from other countries. It is common for Americans to wear casual clothing to school and to greet professors by first name. Nevertheless, good manners and politeness are always appropriate. If you are courteous and polite, and dress a little more formally than your American friends, it will only reflect well on you. However, there are situations and environments in which formality is the norm.
Some businesses require their employees to wear a uniform or a suit.
It would be inappropriate to wear a T-shirt and blue jeans to a job interview. Some of the more prestigious restaurants require a coat and tie. Formal wear is required at weddings and funerals, or any other event with religious overtones. Rid yourself of any preconceived notions of American behavior before you arrive. If you rely on the stereotypes, you will likely put yourself into an awkward and embarrassing situation and offend your American acquaintances.