Extracting functional information from sequencing data is a main question of computational cancer genomics. We present a computational pipeline to characterize how cancers from different tissue types might have acquired canonical cancer hallmarks via preferential genomic alteration of different biological pathways. This is based on SLAPEnrich, a statistical method implemented in an open source R package, to identify pathway-level enrichments of genetic alterations. We used SLAPEnrich and a curated collection of 374 orthogonal pathway gene-sets encompassing 3,915 genes from public resources mapped to 10 canonical cancer hallmarks to characterise the landscape of pathway alterations contributing to the acquisition of different cancer hallmarks in 4,415 patients across 10 cancer types, from The Cancer Genome Atlas. We find that the heterogeneity of the significantly genomically altered pathways within certain hallmarks reflects their established predominance in determined cancer types and their clinical relevance. In addition, although most of the pathway alteration enrichments and hallmark heterogeneities are guided by somatic mutations in established cancer driver genes , when excluding these variants from the analyses, the levels of predominance of the considered hallmarks are strikingly preserved across cancer types. Therefore we propose to use the obtained hallmark heterogeneity signatures as a ground truth to characterise long tails of infrequent genomic alterations across cancer types, and we highlight a number of potential novel cancer driver genes and networks.