The spectrum of gamma-ray burst (GRB) afterglows can be studied with color indices. Here, we present a large comprehensive catalog of 70 GRBs with multiwavelength optical transient data on which we perform a systematic study to find the temporal evolution of color indices. We categorize them into two samples based on how well the color indices are evaluated. The Golden sample includes 25 bursts mostly observed by GROND, and the Silver sample includes 45 bursts observed by other telescopes. For the Golden sample, we find that 96% of the color indices do not vary over time. However, the color indices do vary during short periods in most bursts. The observed variations are consistent with effects of (i) the cooling frequency crossing the studied energy bands in a wind medium (43%) and in a constant-density medium (30%), (ii) early dust extinction (12%), (iii) transition from reverse-shock to forward-shock emission (5%), or (iv) an emergent SN emission (10%). We also study the evolutionary properties of the mean color indices for different emission episodes. We find that 86% of the color indices in the 70 bursts show constancy between consecutive ones. The color index variations occur mainly during the late GRB-SN bump, the flare, and early reverse-shock emission components. We further perform a statistical analysis of various observational properties and model parameters (spectral index beta(CI)(o), electron spectral indices p(CI), etc.) using color indices. Overall, we conclude that similar to 90% of colors are constant in time and can be accounted for by the simplest external forward-shock model, while the varying color indices call for more detailed modeling.