Using U'- through Ks-band imaging data in the Great Observatories Origins Deep Survey-South (GOODS-South) field, we construct a large, complete sample of 275 extremely red objects (EROs; Ks 3.35; AB), all with deep Hubble Space Telescope Advanced Camera for Surveys imaging in B435, V606, i775, and z850 and well-calibrated photometric redshifts. Quantitative concentration and asymmetry measurements fail to separate EROs into distinct morphological classes. We therefore visually classify the morphologies of all EROs into four broad types—early (elliptical-like), late (disk galaxies), irregular, and (chain galaxies and low surface brightness galaxies)—and calculate their relative fractions and comoving space densities. For a broad range of limiting magnitudes and color thresholds, the relative number of early-type EROs is approximately constant at 33%-44%, and the comoving space densities of early- and late-type EROs are comparable. Mean rest-frame spectral energy distributions (SEDs) at λrest ≈ 0.1-1.2 μm are constructed for all EROs. The SEDs are extremely similar in their range of shapes, independent of morphological type. The implication is that any differences between the broadband SEDs of early-type EROs and the other types are relatively subtle, and there is no robust way of photometrically distinguishing between different morphological types with usual optical/near-infrared photometry.