Do I need a passport when traveling in the United States?

If you are coming in from outside the country, yes. Once here, you won't need it to move between the states.

If you are an American citizen with proper I.D. such as a driver's license, NO you don't need a passport but need proper ID in case you are stopped by the police.. If you are flying within the confines of the lower 48 states, then no, you don't need one either, but you will need proper ID in case you are stopped by the security people at the airport or the police.

If you are a foreigner traveling in the US, you will definitely need some form of ID and your passport is an excellent form of ID.

You posted this under air travel so I suspect you are going to be traveling by plane. You don't need a passport to travel within the US as there are no "borders" between each state. Since 9-11 airports are getting stricter about just who they let on planes, so I would suggest having your passport if you are a foreigner to avoid any delays.