Accepted for Publication in Apj

We describe Hubble Space Telescope (HST) imaging of 10 of the 20 ESO Distant Cluster Survey (EDisCS) fields. Each ∼40 square arcminute field was imaged in the F814W filter with the Advanced Camera for Surveys Wide Field Camera. Based on these data, we present visual morphological classifications for the ∼920 sources per field that are brighter than I auto = 23 mag. We use these classifications to quantify the morphological content of 10 intermediate-redshift (0.5 < z < 0.8) galaxy clusters within the HST survey region. The EDisCS results, combined with previously published data from seven higher redshift clusters, show no statistically significant evidence for evolution in the mean fractions of elliptical, S0, and late-type (Sp+Irr) galaxies in clusters over the redshift range 0.5 < z < 1.2. In contrast, existing studies of lower redshift clusters have revealed a factor of ∼2 increase in the typical S0 fraction between z = 0.4 and z = 0, accompanied by a commensurate decrease in the Sp+Irr fraction and no evolution in the elliptical fraction. The EDisCS clusters demonstrate that cluster morphological fractions plateau beyond z ≈ 0.4. They also exhibit a mild correlation between morphological content and cluster velocity dispersion, highlighting the importance of careful sample selection in evaluating evolution. We discuss these findings in the context of a recently proposed scenario in which the fractions of passive (E,S0) and star-forming (Sp,Irr) galaxies are determined primarily by the growth history of clusters.