Outcomes for cancer patients vary greatly even within the same tumor type, and characterization of molecular subtypes of cancer holds important promise for improving prognosis and personalized treatment. This promise has motivated recent efforts to produce large amounts of multidimensional genomic (multi-omic) data, but current algorithms still face challenges in the integrated analysis of such data. Here we present Cancer Integration via Multikernel Learning (CIMLR), a new cancer subtyping method that integrates multi-omic data to reveal molecular subtypes of cancer. We apply CIMLR to multi-omic data from 36 cancer types and show significant improvements in both computational efficiency and ability to extract biologically meaningful cancer subtypes. The discovered subtypes exhibit significant differences in patient survival for 27 of 36 cancer types. Our analysis reveals integrated patterns of gene expression, methylation, point mutations, and copy number changes in multiple cancers and highlights patterns specifically associated with poor patient outcomes.