We examine the variability of the high-ionization C IV λ1549 line in a sample of 105 quasars observed at multiple epochs by the Sloan Digital Sky Survey. We find a strong correlation between the change in the C IV line flux and the change in the line width, but no correlations between the change in flux and changes in line center and skewness. The relation between line flux change and line width change is consistent with a model in which a broad line base varies with greater amplitude than the line core. The objects studied here are more luminous and at higher redshift than those normally studied for variability, ranging in redshift from 1.65 to 4.00 and in absolute r-band magnitude from roughly -24 to -28. Using moment analysis line-fitting techniques, we measure line fluxes, centers, widths, and skewnesses for the C IV line at two epochs for each object. The well-known Baldwin effect is seen for these objects, with a slope of β = -0.22. The sample has a median intrinsic Baldwin effect slope of βint = -0.85; the C IV lines in these high-luminosity quasars appear to be less responsive to continuum variations than those in lower luminosity AGNs. In addition, we find no evidence for variability of the well-known blueshift of the C IV line with respect to the low-ionization Mg II λ2798 line in the highest flux objects, indicating that this blueshift might be useful as a measure of orientation.