Post-transcriptional gene regulation is mediated through complex networks of protein-RNA interactions. The targets of only a few RNA binding proteins (RBPs) are known, even in the well-characterized budding yeast. In silico prediction of protein-RNA interactions is therefore useful to guide experiments and to provide insight into regulatory networks. Computational approaches have identified RBP targets based on sequence binding preferences. We investigate here to what extent RBP-RNA interactions can be predicted based on RBP and mRNA features other than sequence motifs. We analyze global relationships between gene and protein properties in general and between selected RBPs and known mRNA targets in particular. Highly translated RBPs tend to bind to shorter transcripts, and transcripts bound by the same RBP show high expression correlation across different biological conditions. Surprisingly, a given RBP preferentially binds to mRNAs that encode interaction partners for this RBP, suggesting coordinated post-transcriptional auto-regulation of protein complexes. We apply a machine-learning approach to predict specific RBP targets in yeast. Although this approach performs well for RBPs with known targets, predictions for uncharacterized RBPs remain challenging due to limiting experimental data. We also predict targets of fission yeast RBPs, indicating that the suggested framework could be applied to other species once more experimental data are available.