We present results from observations of 29 BL Lacertae objects, taken with the Whipple Observatory 10 m gamma-ray telescope between 1995 and 2000. The observed objects are mostly at low redshift (z < 0.2), but observations of objects of up to z = 0.444 are also reported. Five of the objects are EGRET sources and two are unconfirmed TeV sources. Three of the confirmed sources of extragalactic TeV gamma rays were originally observed as part of this survey and have been reported elsewhere. No significant excesses are detected from any of the other objects observed, on timescales of days, months, or years. We report 99.9% confidence level flux upper limits for the objects for each observing season. The flux upper limits are typically 20% of the Crab flux, although for some sources, limits as sensitive as 6% of the Crab flux were derived. The results are consistent with the synchrotron self-Compton model predictions considered in this work.