We use Keck HIRES spectra of 37 optically bright quasars at z=2-4 to study narrow absorption lines that are intrinsic to the quasars (intrinsic NALs, produced in gas that is physically associated with the quasar central engine). We identify 150 NAL systems, which contain 124 CIV, 12 NV, and 50 SiIV doublets, of which 18 are associated systems (within 5000km/s of the quasar redshift). We use partial coverage analysis to separate intrinsic NALs from NALs produced in cosmologically intervening structures. We find 39 candidate intrinsic systems (28 reliable determinations and 11 that are possibly intrinsic). We estimate that 10%-17% of CIV systems at blueshifts of 5000-70000km/s relative to quasars are intrinsic. At least 32% of quasars contain one or more intrinsic CIV NALs. Considering NV and SiIV doublets showing partial coverage as well, at least 50% of quasars host intrinsic NALs.