The airplane experienced an engine failure due to fuel exhaustion while on final between the FAF and the threshold on a second ILS approach in night IMC after a flight of 5.1 hours. A missed approach was executed on the first when the pilot deviated beyond limits both in altitude and course. The pilot had flight planned 3:45 ETE and indicated that he had 6:00 hours of fuel on board. The fuel exhaustion time corresponded with performance data provided in the airplane owner's handbook. Although he received a weather briefing prior to departure and obtained weather en route, the pilot did not request wind aloft information. The flight encountered 35 to 40 knot head winds throughout the trip and on 4 separate occasions the controllers asked the pilot if he had enough fuel to reach his destination. During the final leg of the flight the pilot overflew at least 3 suitable alternate airports. Following the engine failure, the pilot allowed the airplane to stall and it subsequently impacted the ground in steep nose down, left wing leading attitude.