Cancer therapy is challenged by the diversity of molecular implementations of oncogenic processes and by the resulting variation in therapeutic responses. Projects such as The Cancer Genome Atlas (TCGA) provide molecular tumor maps in unprecedented detail. The interpretation of these maps remains a major challenge. Here we distilled thousands of genetic and epigenetic features altered in cancers to ~500 selected functional events (SFEs). Using this simplified description, we derived a hierarchical classification of 3,299 TCGA tumors from 12 cancer types. The top classes are dominated by either mutations (M class) or copy number changes (C class). This distinction is clearest at the extremes of genomic instability, indicating the presence of different oncogenic processes. The full hierarchy shows functional event patterns characteristic of multiple cross-tissue groups of tumors, termed oncogenic signature classes. Targetable functional events in a tumor class are suggestive of class-specific combination therapy. These results may assist in the definition of clinical trials to match actionable oncogenic signatures with personalized therapies.