Intra-tumor heterogeneity is a major obstacle to cancer treatment. Existing single-cell studies of intra-tumor heterogeneity have largely focused on DNA mutations; functional heterogeneity is thus less well understood. We performed an unbiased analysis of functional diversity in colorectal cancer cells and their microenvironment using RNA-seq profiling of over 1,500 unsorted single cells from 11 primary tumors and matched normal mucosa (NM). To robustly interpret single-cell transcriptomes, we developed novel algorithms for normalizing expression estimates (pQ), clustering cells (RCA) and identifying differentially expressed genes (NODES). RCA identified 6 major cell types and multiple subtypes within colorectal samples. Single-cell differential expression analysis yielded results that were substantially different from bulk-sample analysis. Notably, epithelial-mesenchymal transition (EMT) genes were upregulated in tumor fibroblasts, but not in cancer cells. Though cancer cells generally lay on a continuum of transcriptomic states, a small "tail" of cells showed exceptionally high stemness signatures. Importantly, colorectal tumors previously assigned to a single subtype based on bulk transcriptomics could be divided into subgroups with divergent survival probability based on single-cell signatures, thus underscoring the prognostic value of our approach. Going forward, we see single-cell transcriptomics becoming an essential tool for cancer biology, biomarker discovery and personalized oncology.