The private pilot said he departed with approximately 55 gallons of fuel on board (about 3.5 hours total) and departed on a long cross country flight. Approximately three hours and 30 minutes into the flight, while on an ILS approach into his destination airport in VFR conditions, the pilot said the engine suddenly stopped but the propeller continued to windmill. He pumped the throttle, and finally pushed it full forward, but there was still no thrust. He checked the engine guages and they were normal, but he did not look at the fuel guages. A witness heard the engine sputtering as it flew overhead. The pilot was unable to maintain altitude and attempted to reach a field, but ended up colliding with the roof of a private residence. The airplane came to rest in the residence's backyard. The pilot reported not seeing any fuel leaks or streaks when he got out of the airplane. Examination of the airplane revealed there was no fuel in either wing tank, and there was no staining of the grass or foliage surrounding the airplane. When the airplane wing's were removed for salvage, less than one-pint of fuel was drained from the fuel lines.