  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.
