We propose Bayesian nonparametric methodology to model error distribution in an additive quantile regression setting. Bayesian modeling enables full inference not only for the model parameters, but for any functional of interest of the response distribution. Moreover, nonparametric prior probability models allow the shape of error density to adapt to data, so provide more reliable predictive inference than models based on parametric error distributions. We develop three models based on Dirichlet process mixtures of uniform densities, which can capture the shape of any unimodal error density. The models are further extended to handle censored observations. We also develop quantile regression models, which allow the error distribution to change nonparametrically with the covariates. We use Markov chain Monte Carlo techniques for posterior simulation.