We study residual plots for parametric accelerated failure time (AFT) models, using both standardized residuals and Cox-Snell residuals. Two different approaches are discussed in the case of censored data; adjusting censored residuals by adding a residual time, and using nonparametric exponential regression of non-adjusted censored Cox-Snell residuals. The main object of the paper is to show how residuals can be used to infer the correct functional form for possibly misspecified covariates. We demonstrate the use of the methods by analysis of two reliability data sets and by a simulation study using Weibull-distributed data. We also consider briefly a corresponding approach for parametric proportional hazards models.