We report the discovery of significant localized structures in the projected two-dimensional spatial distributions of the Globular Cluster (GC) systems of the 10 brightest galaxies in the Virgo Cluster. We use catalogs of GCs extracted from the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) Virgo Cluster Survey (ACSVCS) imaging data, complemented, when available, by additional archival ACS data. These structures have projected sizes ranging from ∼5″ to a few arcminutes (∼1 to ∼25 kpc). Their morphologies range from localized, circular to coherent, complex shapes resembling arcs and streams. The largest structures are preferentially aligned with the major axis of the host galaxy. A few relatively smaller structures follow the minor axis. Differences in the shape and significance of the