Using a sample of 3814 quasars from the Early Data Release of the Sloan Digital Sky Survey, we confirm that high-ionization, broad emission lines, such as C IV, are significantly blueshifted with respect to low-ionization, broad emission lines, such as Mg II, which are thought to be close to the systemic redshift. We examine the velocity shifts of the Mg II and C IV emission lines with respect to [O III] and Mg II, respectively. C IV emission-line peaks have a range of shifts from a redshift of 500 km s^-1 to blueshifts well in excess of 2000 km s^-1 as compared with Mg II. We confirm previous results that suggest an anticorrelation between the shift of the C IV emission-line peak and the rest equivalent width of the C IV emission line. Furthermore, by creating composite quasar spectra as a function of C IV shift, we are able to study in detail the profiles of the line as a function of velocity shift. We find that the apparent shift of the C IV emission-line peak is not a shift so much as it is a lack of flux in the red wing for the composite with the largest apparent shift. This observation should strongly constrain models for the broad emission-line region in quasars. The emission-line blueshift and equivalent width of C IV are also discussed in light of the well-known anticorrelation between the equivalent width of C IV emission and continuum luminosity, otherwise known as the Baldwin effect. We further discuss the C IV emission-line shift as a function of other quasar properties, such as spectral index, radio and X-ray detection. We find a possible correlation between the C IV emission-line shifts and the radio properties of the quasars, which is suggestive of orientation as the cause of the C IV velocity shifts. Finally, we explore whether the C IV emission-line blueshifts correlate with the presence of broad absorption line absorption troughs or with narrow, "associated" absorption, and how these might be related to orientation.