We perform a systematic search for long-term extreme variability quasars (EVQs) in the overlapping Sloan Digital Sky Survey (SDSS) and 3-Year Dark Energy Survey (DES) imaging, which provide light curves spanning more than 15 years. We identified ~1000 EVQs with a maximum g band magnitude change of more than 1 mag over this period, about 10% of all quasars searched. The EVQs have L_bol~10^45-10^47 erg/s and L/L_Edd~0.01-1. Accounting for selection effects, we estimate an intrinsic EVQ fraction of ~30-50% among all g<~22 quasars over a baseline of ~15 years. These EVQs are good candidates for so-called changing-look quasars, where a spectral transition between the two types of quasars (broad-line and narrow-line) is observed between the dim and bright states. We performed detailed multi-wavelength, spectral and variability analyses for the EVQs and compared to their parent quasar sample. We found that EVQs are distinct from a control sample of quasars matched in redshift and optical luminosity: (1) their UV broad emission lines have larger equivalent widths; (2) their Eddington ratios are systematically lower; and (3) they are more variable on all timescales. The intrinsic difference in quasar properties for EVQs suggest that internal processes associated with accretion are the main driver for the observed extreme long-term variability. However, despite their different properties, EVQs seem to be in the tail of a continuous distribution of quasar properties, rather than standing out as a distinct population. We speculate that EVQs are normal quasars accreting at relatively low accretion rates, where the accretion flow is more likely to experience instabilities that drive the factor of few changes in flux on multi-year timescales.
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