We present the results of a search for untriggered gamma-ray burst ( GRB ) afterglows with the Robotic Optical Transient Search Experiment-III ( ROTSE-III ) telescope array . This search covers observations from September 2003 to March 2005 . We have an effective coverage of 1.74 \mathrm { deg } ^ { 2 } \mathrm { yr } for rapidly fading transients that remain brighter than \sim 17.5 magnitude for more than 30 minutes . This search is the first large area survey to be able to detect typical untriggered GRB afterglows . Our background rate is very low and purely astrophysical . We have found 4 previously unknown cataclysmic variables ( CVs ) and 1 new flare star . We have not detected any candidate afterglow events or other unidentified transients . We can place an upper limit on the rate of fading optical transients with quiescent counterparts dimmer than \sim 20 ^ { th } magnitude at a rate of less than 1.9 \mathrm { deg } ^ { -2 } \mathrm { yr } ^ { -1 } with 95 % confidence . This places limits on the optical characteristics of off-axis ( orphan ) GRB afterglows . As a byproduct of this search , we have an effective \sim 52 \mathrm { deg } ^ { 2 } \mathrm { yr } of coverage for very slowly decaying transients , such as CVs . This implies an overall rate of outbursts from high galactic latitude CVs of 0.1 \mathrm { deg } ^ { -2 } \mathrm { yr } ^ { -1 } .