The pilot of the Cessna 177B stated that he was attempting a long cross-country flight, with a planned fuel stop at an airport about halfway to his intended destination. While enroute to the planned fuel stop, the airplane consumed more fuel than planned due to greater than forecast headwinds. The pilot also elected to fly at a lower than planned altitude, in order to avoid turbulence. Although the flight was consuming more fuel than planned, the pilot believed that an adequate amount of fuel remained to fly to the planned fuel stop and beyond. After landing uneventfully for the planned fuel stop, the pilot was informed that the airport fixed base operator had run out of fuel. The pilot then elected to depart, and refuel the airplane at an airport about 10 miles away. While on final approach to that airport, the engine lost all power, and the pilot performed a forced landing into trees. The pilot sustained serious injuries, the two passengers sustained minor injuries, and the airplane's left wing separated. Examination of the wreckage by a Federal Aviation Administration inspector revealed that approximately 3.5 total gallons of aviation fuel was recovered from the airplane's four fuel tanks. The inspector also examined the engine, and did not observe any preimpact mechanical malfunctions, nor did the pilot report any.