We present observations of the dwarf galaxies Draco and Ursa Minor, the Local Group galaxies M32 and M33, and the globular cluster M15 conducted with the Whipple 10 m gamma-ray telescope to search for the gamma-ray signature of self-annihilating weakly interacting massive particles (WIMPs), which may constitute astrophysical dark matter (DM). We review the motivations for selecting these sources based on their unique astrophysical environments and report the results of the data analysis that produced upper limits on the excess rate of gamma rays for each source. We consider models for the DM distribution in each source based on the available observational constraints and discuss possible scenarios for the enhancement of the gamma-ray luminosity. Limits on the thermally averaged product of the total self-annihilation cross section and velocity of the WIMP, ⟨συ⟩ , are derived using conservative estimates for the magnitude of the astrophysical contribution to the gamma-ray flux. Although these limits do not constrain predictions from the currently favored theoretical models of supersymmetry (SUSY), future observations with VERITAS will probe a larger region of the WIMP parameter phase space, ⟨συ⟩ , and WIMP particle mass (mχ).