We report on a complete set of early optical afterglows of gamma-ray bursts (GRBs) obtained with the Robotic Optical Transient Search Experiment (ROTSE-III) telescope network from 2005 March through 2007 June. This set is comprised of 12 afterglows with early optical and Swift/X-Ray Telescope observations, with a median ROTSE-III response time of 45 s after the start of gamma-ray emission (8 s after the GCN notice time). These afterglows span 4 orders of magnitude in optical luminosity, and the contemporaneous X-ray detections allow multi-wavelength spectral analysis. Excluding X-ray flares, the broadband synchrotron spectra show that the optical and X-ray emission originate in a common region, consistent with predictions of the external forward shock in the fireball model. However, the fireball model is inadequate to predict the temporal decay indices of the early afterglows, even after accounting for possible long-duration continuous energy injection. We find that the optical afterglow is a clean tracer of the forward shock, and we use the peak time of the forward shock to estimate the initial bulk Lorentz factor of the GRB outflow, and find 100 less than or similar to Gamma(0) less than or similar to 1000, consistent with expectations.