We investigate biases in the measurement of exoplanet orbital parameters - especially eccentricity - from radial velocity (RV) observations. In this contribution we consider single-planet systems. We create a mock catalog of RV data, choosing planet masses and orbital periods, and observing patterns to mimic those of actual RV surveys. Using Markov chain Monte Carlo (MCMC) simulations, we generate a posterior sample for each mock data set, calculate best-fit orbital parameters for each data set, and compare these to the true values. We find that the precision of our derived eccentricities is most closely related to the effective signal-to-noise ratio, K√N/σ, where K is the velocity amplitude, cr is the effective single-measurement precision, and N is the number of observations. We also find that eccentricities of planets on nearly circular (e < 0.05) orbits are preferentially overestimated. While the Butler et al. (2006) catalog reports e < 0.05 for just 20% of its planets, we estimate that the true fraction of e < 0.05 orbits is about 50%. We investigate the accuracy, precision, and bias of alternative sets of summary statistics and find that the median values of h = esinω and k = ecosω (where ω is the longitude of periapse) of the posterior sample typically provide more accurate, more precise, and less biased estimates of eccentricity than traditional measures.