  We present a new and simple technique for selecting extensive, complete and
pure quasar samples, based on their intrinsic variability. We parametrize the
single-band variability by a power-law model for the light-curve structure
function, with amplitude A and power-law index gamma. We show that quasars can
be efficiently separated from other non-variable and variable sources by the
location of the individual sources in the A-gamma plane. We use ~60 epochs of
imaging data, taken over ~5 years, from the SDSS stripe 82 (S82) survey, where
extensive spectroscopy provides a reference sample of quasars, to demonstrate
the power of variability as a quasar classifier in multi-epoch surveys. For
UV-excess selected objects, variability performs just as well as the standard
SDSS color selection, identifying quasars with a completeness of 90% and a
purity of 95%. In the redshift range 2.5<z<3, where color selection is known to
be problematic, variability can select quasars with a completeness of 90% and a
purity of 96%. This is a factor of 5-10 times more pure than existing
color-selection of quasars in this redshift range. Selecting objects from a
broad griz color box without u-band information, variability selection in S82
can afford completeness and purity of 92%, despite a factor of 30 more
contaminants than quasars in the color-selected feeder sample. This confirms
that the fraction of quasars hidden in the 'stellar locus' of color-space is
small. To test variability selection in the context of Pan-STARRS 1 (PS1) we
created mock PS1 data by down-sampling the S82 data to just 6 epochs over 3
years. Even with this much sparser time sampling, variability is an
encouragingly efficient classifier. For instance, a 92% pure and 44% complete
quasar candidate sample is attainable from the above $griz$-selected catalog.
