I am going on a semester-long trip to the east, and I want a soap that I can use in my hair, body and even to wash my clothes. One good choice is the family of No-Rinse cleaners from Rivard International. These work just as described, requiring no water to rinse out the soap. They're what folks on the space shuttle use to keep a little clean between landings on earth. No-Rinse comes in several iterations, including a Body Bath and Shampoo.
Cost is about four dollars for an eight-ounce bottle.
The stuff is available from Campmor, among many other retailers. If water is at hand, another good product is Sunshower Soap, made by the folks who make the Sunshower portable camping shower. Costs is about four dollars for a four-ounce bottle. Lastly, I'd be sure to pack along a good quantity of waterless hand cleanser, and use it regularly. One good one is the germsAside waterless hand cleanser from the Kiss My Face company, about five dollars for a four-ounce bottle.