Although a large number of clustering algorithms have been proposed to identify groups of co-expressed genes from microarray data, the question of if and how such methods may be applied to RNA-seq data remains unaddressed. In this work, we investigate the use of data transformations in conjunction with Gaussian mixture models for RNA-seq co-expression analyses, as well as a penalized model selection criterion to select both an appropriate transformation and number of clusters present in the data. This approach has the advantage of accounting for per-cluster correlation structures among samples, which can be quite strong in real RNA-seq data. In addition, it provides a rigorous statistical framework for parameter estimation, an objective assessment of data transformations and number of clusters, and the possibility of performing diagnostic checks on the quality and homogeneity of the identified clusters. We analyze four varied RNA-seq datasets to illustrate the use of transformations and model selection in conjunction with Gaussian mixture models. Finally, we propose an R package coseq (co-expression of RNA-seq data) to facilitate implementation and visualization of the recommended RNA-seq co-expression analyses.