Clustering and classification of replicated data is often performed using classical techniques that inappropriately treat the data as unreplicated, or by complex modern ones that are computationally demanding. In this paper, we introduce a simple approach based on a spike-and-slab mixture model that is fast, automatic, allows classification, clustering and variable selection in a single framework, and can handle replicated or unreplicated data. Simulation shows that our approach compares well with other recently proposed methods. The ideas are illustrated by application to microarray and metabolomic data. The Canadian Journal of Statistics 43: 157-175; 2015 (c) 2015 Statistical Society of Canada