Robust regression techniques are a class of estimators that are relatively insensitive to the presence of one or more outliers in the data. They are especially well suited to data that require large numbers of statistical tests and may contain outliers due to factors not of experimental interest. Both these issues apply particularly to neuroimaging data analysis. We use simulations to compare several robust techniques against ordinary least squares (OLS) regression, and we apply robust regression to second-level (group "random effects") analyses in three fMRI datasets. Our results show that robust iteratively reweighted least squares (IRLS) at the 2nd level is a computationally efficient technique that both increases statistical power and decreases false positive rates in the presence of outliers. The benefits of IRLS are apparent with small samples (n = 10) and increase with larger sample sizes (n = 40) in the typical range of group neuroimaging experiments. When no true effects are present, IRLS controls false positive rates at an appropriate level. We show that IRLS can have substantial benefits in analysis of group data and in estimating hemodynamic response shapes from time series data. We provide software to implement IRLS in group neuroimaging analyses.