Cancer arises as a consequence of cumulative disruptions to cellular growth control with selection for those heritable changes that provide the greatest clonal advantage. These traits can be acquired and stably maintained by either genetic or epigenetic means. It is now clear that the cancer genome and epigenome influence each other in multiple ways. For example, mutation of the IDH1 gene results in the accumulation of a novel oncometabolite, 2-hydroxyglutarate, which is associated with an extensive CpG island methylator phenotype (CIMP) in glioblastoma and acute myeloid leukemia. As part of the Cancer Genome Atlas (TCGA) project, we performed an analysis of DNA methylation alterations in more than 10,000 primary human cancer specimens spanning 33 cancer types. We found that predisposition to DNA methylation gains (hypermethylation) was linked primarily to polycomb repressive complex occupancy in precursor tissues, consistent with an epigenetic block to cellular differentiation as an early or even initiating event in carcinogenesis. On the other hand, widespread loss of DNA methylation (hypomethylation) is linked to replication-associated progressive erosion of DNA methylation at late-replicating, lamina-associated domains in the genome located at the nuclear periphery. We show that this phenomenon can be used to develop a molecular mitotic clock. Disruption of epigenomic control is pervasive in malignancy, with extensive phenotypic consequences, and should thus be considered an enabling characteristic of cancer cells, akin to genome instability and mutation.