The conductance of a single molecule connected to two gold electrodes was determined by repeatedly forming thousands of gold-molecule-gold junctions. Conductance histograms revealed well-defined peaks at integer multiples of a fundamental conductance value, which was used to identify the conductance of a single molecule. The resistances near zero bias were 10.5 +/- 0.5, 51 +/- 5, 630 +/- 50, and 1.3 +/- 0.1 megohms for hexanedithiol, octanedithiol, decanedithiol, and 4,4' bipyridine, respectively. The tunneling decay constant (betaN) for N-alkanedithiols was 1.0 +/- 0.1 per carbon atom and was weakly dependent on the applied bias. The resistance and betaN values are consistent with first-principles calculations.