  We provide a quantitative description and statistical interpretation of the
optical continuum variability of quasars. The Sloan Digital Sky Survey (SDSS)
has obtained repeated imaging in five UV-to-IR photometric bands for 33,881
spectroscopically confirmed quasars. About 10,000 quasars have an average of 60
observations in each band obtained over a decade along Stripe 82 (S82), whereas
the remaining ~25,000 have 2-3 observations due to scan overlaps. The observed
time lags span the range from a day to almost 10 years, and constrain quasar
variability at rest-frame time lags of up to 4 years, and at rest-frame
wavelengths from 1000A to 6000A. We publicly release a user-friendly catalog of
quasars from the SDSS Data Release 7 that have been observed at least twice in
SDSS or once in both SDSS and the Palomar Observatory Sky Survey, and we use it
to analyze the ensemble properties of quasar variability. Based on a damped
random walk (DRW) model defined by a characteristic time scale and an
asymptotic variability amplitude that scale with the luminosity, black hole
mass, and rest wavelength for individual quasars calibrated in S82, we can
fully explain the ensemble variability statistics of the non-S82 quasars such
as the exponential distribution of large magnitude changes. All available data
are consistent with the DRW model as a viable description of the optical
continuum variability of quasars on time scales of ~5-2000 days in the rest
frame. We use these models to predict the incidence of quasar contamination in
transient surveys such as those from PTF and LSST.
