We present mass functions of distant actively accreting supermassive black holes residing in luminous quasars discovered in the Large Bright Quasar Survey, the Bright Quasar Survey, and the Fall Equatorial Stripe of the Sloan Digital Sky Survey (SDSS). The quasars cover a wide range of redshifts (0 ~ 10^8 Msun) between redshifts ~4 and ~2.5. Also, the z~4 SDSS quasar mass function has a somewhat flatter high mass-end slope, beta = -1.75 +- 0.56, compared to the mass functions based on quasars below z of 3, which display typical slopes of beta =~ -3.3; the latter are consistent with the mass functions at similar redshifts based on the SDSS Data Release 3 quasar catalog presented by Vestergaard et al. We see clear evidence of cosmic downsizing in the comoving space density distribution of active black holes in the LBQS sample alone. In forthcoming papers, further analysis, comparison, and discussion of these mass functions will be made with other existing black hole mass functions, notably that based on the SDSS DR3 quasar catalog. We present the relationships used to estimate the black hole mass based on the MgII emission line; the relations are calibrated to the Hbeta and CIV relations by means of several thousand high quality SDSS spectra. Mass estimates of the individual black holes of these samples are also presented.