  We report the results of a ${\sim}4$-year direct imaging survey of 104 stars
to resolve and characterize circumstellar debris disks in scattered light as
part of the Gemini Planet Imager Exoplanet Survey. We targeted nearby
(${\lesssim}150$ pc), young (${\lesssim}500$ Myr) stars with high infrared
excesses ($L_{\mathrm{IR}} / L_\star > 10^{-5}$), including 38 with previously
resolved disks. Observations were made using the Gemini Planet Imager
high-contrast integral field spectrograph in $H$-band (1.6 $\mu$m)
coronagraphic polarimetry mode to measure both polarized and total intensities.
We resolved 26 debris disks and three protoplanetary/transitional disks. Seven
debris disks were resolved in scattered light for the first time, including
newly presented HD 117214 and HD 156623, and we quantified basic morphologies
of five of them using radiative transfer models. All of our detected debris
disks but HD 156623 have dust-poor inner holes, and their scattered-light radii
are generally larger than corresponding radii measured from resolved thermal
emission and those inferred from spectral energy distributions. To assess
sensitivity, we report contrasts and consider causes of non-detections.
Detections were strongly correlated with high IR excess and high inclination,
although polarimetry outperformed total intensity angular differential imaging
for detecting low inclination disks (${\lesssim} 70 \deg$). Based on
post-survey statistics, we improved upon our pre-survey target prioritization
metric predicting polarimetric disk detectability. We also examined
scattered-light disks in the contexts of gas, far-IR, and millimeter
detections. Comparing $H$-band and ALMA fluxes for two disks revealed tentative
evidence for differing grain properties. Finally, we found no preference for
debris disks to be detected in scattered light if wide-separation substellar
companions were present.
