Existing high-throughput methods to identify RNA-binding proteins (RBPs) are based on capture of polyadenylated RNAs and cannot recover proteins that interact with nonadenylated RNAs, including long noncoding RNA, pre-mRNAs and bacterial RNAs. We present orthogonal organic phase separation (OOPS), which does not require molecular tagging or capture of polyadenylated RNA, and apply it to recover cross-linked protein-RNA and free protein, or protein-bound RNA and free RNA, in an unbiased way. We validated OOPS in HEK293, U2OS and MCF10A human cell lines, and show that 96% of proteins recovered were bound to RNA. We show that all long RNAs can be cross-linked to proteins, and recovered 1,838 RBPs, including 926 putative novel RBPs. OOPS is approximately 100-fold more efficient than existing methods and can enable analyses of dynamic RNA-protein interactions. We also characterize dynamic changes in RNA-protein interactions in mammalian cells following nocodazole arrest, and present a bacterial RNA-interactome for Escherichia coli. OOPS is compatible with downstream proteomics and RNA sequencing, and can be applied in any organism.