Nereid is a small irregular moon of Neptune that displays large-, moderate-, and small-amplitude photometric variations on both fast and slow time scales. The central mystery of Nereid is now to explain the physical mechanism of these unique brightness changes and why they change with time. To characterize Nereid's variability, we have been using the SMARTS telescopes on Cerro Tololo for synoptic monitoring from 1999 to 2006. We present a well-sampled photometric time series of 493 magnitudes on 246 nights mostly in the V-band. In combination with our earlier data (for 774 magnitudes over 362 nights), our 20-year data set is the most comprehensive for any small icy body in our Solar System. Our yearly light curves show that Nereid displays various types of behaviors: large amplitude brightenings and fadings (1987 to 1990); moderate-amplitude variation about the average phase curve (1993-1997, 2003, 2005), moderate-amplitude variation and systematically brighter by roughly one-quarter magnitude throughout the entire season (2004); and nearly constant light curves superimposed on a surprisingly large-amplitude opposition surge (1998, 1999, 2000, 2006). Other than in 2004, Nereid's variations were closely centered around a constant phase curve that is well fit with a Hapke model for the coherent backscattering opposition surge mechanism with angular scale of 0.7°±0.1°. In our entire data set from 1987-2006, we find no significant periodicity. We propose that the year-to-year changes in the variability of Nereid are caused by forced precession (caused by tidal forces from Neptune) on the spin axis of a nonspherical Nereid, such that cross-sectional areas and average albedos change as viewed from Earth.