  We present evidence that the majority of rapidly-, well-localized gamma-ray
bursts with undetected, or dark, optical afterglows, or `dark bursts' for
short, are most likely the result of extinction by dust in the circumburst
medium. First, we show that the dark bursts cannot be explained by a failure to
image deeply enough quickly enough: We fit a variety of brightness distribution
models to the optical data, and find that approx. 57(+13,-11)% of all bursts,
and approx. 82(+22,-17)% of dark bursts, have afterglows that are fainter than
R = 24 mag 18 hours after the burst. Secondly, we show that dark bursts tend to
be X-ray and radio faint. Thirdly, we show that these correlations, and more
specifically the optical vs. X-ray and optical vs. radio distributions, can be
explained within the framework of the relativistic fireball model if the dark
bursts are extinguished by circumburst dust, and the density of the circumburst
medium spans many orders of magnitude, from densities that are typical of the
Galactic disk to densities that are typical of dense clouds. Finally, we show
that Galactic extinction, host galaxy extinction unrelated to the circumburst
medium, and the following high redshift effects - Lyman limit absorption in the
source frame, absorption by the Ly-alpha forest, absorption by excited
molecular hydrogen in the circumburst medium, and source-frame extinction by
the FUV component of the extinction curve - might contribute to the number of
dark bursts, but only in small numbers.
