We perform a set of high-resolution, fully self-consistent dissipationless N-body simulations to investigate the influence of cold dark matter (CDM) substructure on the dynamical evolution of thin galactic disks. Our method combines cosmological simulations of galaxy-sized CDM halos to derive the properties of substructure populations and controlled numerical experiments of consecutive subhalo impacts onto initially-thin, fully-formed disk galaxies. We demonstrate that close encounters between massive subhalos and galactic disks since z ~ 1 should be common occurrences in ΛCDM models. In contrast, extremely few satellites in present-day CDM halos are likely to have a significant impact on the disk structure. One typical host halo merger history is used to seed controlled N-body experiments of subhalo-disk encounters. As a result of these accretion events, the disk thickens considerably at all radii with the disk scale height increasing in excess of a factor of 2 in the solar neighborhood. We show that interactions with the subhalo population produce a wealth of distinctive morphological signatures in the disk stars, many of which resemble those being discovered in the Milky Way (MW), M31, and in other disk galaxies, including: conspicuous flares; bars; low-lived, ring-like features in the outskirts; and low-density, filamentary structures above the disk plane. These findings highlight the significant role of CDM substructure in setting the structure of disk galaxies and driving galaxy evolution.