  This paper presents an investigation into the gravitational microlensing of
quasars by stars and stellar remnants in the Milky Way. We present predictions
for the all-sky microlensing optical depth, time-scale distributions and event
rates for future large-area sky surveys. As expected, the total event rate
increases rapidly with increasing magnitude limit, reflecting the fact that the
number density of quasars is a steep function of magnitude. Surveys such as
Pan-STARRS and LSST should be able to detect more than ten events per year,
with typical event durations of around one month. Since microlensing of quasar
sources suffers from fewer degeneracies than lensing of Milky Way sources, they
could be used as a powerful tool for recovering the mass of the lensing object
in a robust, often model-independent, manner. As a consequence, for a subset of
these events it will be possible to directly `weigh' the star (or stellar
remnant) that is causing the lensing signal, either through higher order
microlensing effects and/or high-precision astrometric observations of the lens
star (using, for example, Gaia or SIM-lite). This means that such events could
play a crucial role in stellar astronomy. Given the current operational
timelines for Pan-STARRS and LSST, by the end of the decade they could
potentially detect up to 100 events. Although this is still too few events to
place detailed constraints on Galactic models, consistency checks can be
carried out and such samples could lead to exciting and unexpected discoveries.
