ACFT stalled & crashed after a pwr loss during night x-country flt. Plt radioed a 'mayday' call after reporting 3 mins earlier he had 30-45 mins of fuel remaining. Indianapolis ARTCC was giving flt assistance to N3639Q & advised the flt of an arpt at 'your two o'clock position and 3 miles.' This occurred after some discussion, which started at 0522:45, about the flts low fuel state and fuel remaining vs distance to Evansville. HUF sector advised at 0530:51, 'There are several, uh, smaller arpts along the way there if you, uh, need to go down, let us know.' Plt made no decision at this time. At 0535:38, plt was again questioned about fuel and advised that his estimate of fuel remaining was cautionary for the remaining distance to destination. Plt confirmed that enough fuel remained. At 0538:35, plt transmitted, '39Quebec out of gas. Going down at this time.' The plt continued to communicate by radio and was vectored toward an arpt. Aprx 1 min after the arpt was sighted, radio contact was lost.