The 2.4m Hiltner Telescope at MDM Observatory was used in an attempt to measure trigonometric parallaxes for 14 cataclysmic variable stars. Techniques are described in detail. In the best cases the parallax uncertainties are below 1mas, and significant parallaxes are found for most of the program stars. A Bayesian method that combines the parallaxes together with proper motions and absolute magnitude constraints is developed and used to derive distance estimates and confidence intervals. The most precise distance derived here is for WZ Sge, for which is found to be 43.3^+1.6^_-1.5_pc. Six Luyten Half-Second stars with previous precise parallax measurements were remeasured to test the techniques, and good agreement was found.