VERITAS is a ground-based imaging atmospheric Cherenkov telescope array sensitive to very high energy (VHE, E > 100 GeV) gamma rays. VERITAS has detected VHE gamma-ray emission from nearly 60 astrophysical sources of varied source classes. One of the primary areas of research of VERITAS is the study of galactic particle accelerators, and among the classes of galactic objects investigated are pulsars, binary systems, and pulsar wind nebulae. In this contribution, recent results from VERITAS on the three aforementioned source classes will be presented, including: results from a search for pulsed emission from 14 young pulsars appearing in archival VERITAS data; observations of the binary system PSR J2032+4127/MT91 213, which is quickly approaching its periastron passage set to occur in 2017 November; and follow-up observations of new VHE gamma-ray sources detected by the HAWC observatory. These VERITAS observations will provide insight into the particle acceleration and radiation mechanisms at work in these galactic objects.