Using the 2MASS Second Incremental Data Release (Cat. <B/2mass>), we have searched for near-infrared counterparts to 13214 quasars from the Veron-Cetty & Veron (Cat. <VII/215>) catalog. We have detected counterparts within 4" for 2277 of the approximately 6320 quasars within the area covered by the 2MASS Second Incremental Data Release. Only 1.6% of these are expected to be chance coincidences. Though this sample is heterogeneous, we find that known radio-loud quasars are more likely to have large near-infrared-to-optical luminosity ratios than radio-quiet quasars are, at a statistically significant level. This is consistent with dust-reddened quasars being more common in radio-selected samples than in optically selected samples, due to stronger selection effects against dust-reddened quasars in the latter. We also find a statistically significant dearth of optically luminous quasars with large near-infrared-to-optical luminosity ratios. This can be explained in a dust obscuration model but not in a model where synchrotron emission extends from the radio into the near-infrared and creates such large ratios. We also find that selection of quasar candidates from the B-J/J-K color-color diagram, modeled on the V-J/J-K selection method of Warren, Hewett, & Foltz, is likely to be more sensitive to dust-obscured quasars than selection using only infrared-infrared colors.