We report the discovery of 10 proplyd-like objects in the vicinity of the massive OB association Cygnus OB2. They were discovered in IPHAS Hα images and are clearly resolved in broadband Hubble Space Telescope/Advanced Camera for Surveys, near-IR, and Spitzer mid-IR images. All exhibit the familiar tadpole shape seen in photoevaporating objects such as the Orion proplyds, with a bright ionization front at the head facing the central cluster of massive stars and a tail stretching in the opposite direction. Many also show secondary ionization fronts, complex tail morphologies, or multiple heads. We consider the evidence that these are either proplyds or "evaporating gaseous globules" (EGGs) left over from a fragmenting molecular cloud, but find that neither scenario fully explains the observations. Typical sizes are 50,000-100,000 AU, larger than the Orion proplyds, but in agreement with the theoretical scaling of proplyd size with distance from the ionizing source. These objects are located at projected separations of ~6-14 pc from the OB association, compared to ~0.1 pc for the Orion proplyds, but are clearly being photoionized by the ~65 O-type stars in Cyg OB2. Central star candidates are identified in near- and mid-IR images, supporting the proplyd scenario, though their large sizes and notable asymmetries are more consistent with the EGG scenario. A third possibility is therefore considered that these are a unique class of photoevaporating partially embedded young stellar objects that have survived the destruction of their natal molecular cloud. This has implications for the properties of stars that form in the vicinity of massive stars.