  We characterize the optical counterparts to the compact X-ray source
population within the nearby spiral galaxy M81 using multi-band Hubble Space
Telescope (HST) imaging data. By comparing the optical luminosities and colors
measured for candidate donor stars and host clusters to stellar and cluster
evolutionary models, respectively, we estimate the likely masses and upper age
limits of the field and cluster X-ray binaries. We identify 15 low-mass X-ray
binaries (i.e. donor star mass $\leq$ 3 solar masses) within ancient globular
clusters, as well as 42 candidate high-mass X-ray binaries (i.e. donor star
mass $\geq$ 8 solar masses). To estimate the likelihood of misclassifications,
we inject 4,000 artificial sources into the HST mosaic image and conclude that
our classifications of globular clusters and high-mass X-ray binaries are
reliable at the >90% level. We find that globular clusters that host X-ray
binaries are on average more massive and more compact than globular clusters
that do not. However, there is no apparent correlation between the X-ray
brightness of the clusters and their masses or densities, nor are X-ray binary
hosts more X-ray luminous than the general field population of low-mass X-ray
binaries. This work represents one of the first in-depth analyses of the
population of X-ray binaries within globular clusters in a spiral galaxy.
