Viruses cause 10-15% of all human cancers. Massively parallel sequencing has recently proved effective for uncovering novel viruses and virus-tumour associations, but this approach has not yet been applied to comprehensive patient cohorts. Here we screen a diverse landscape of human cancer, encompassing 4,433 tumours and 19 cancer types, for known and novel expressed viruses based on >700 billion transcriptome sequencing reads from The Cancer Genome Atlas Research Network. The resulting map confirms and extends current knowledge. We observe recurrent fusion events, including human papillomavirus insertions in RAD51B and ERBB2. Patterns of coadaptation between host and viral gene expression give clues to papillomavirus oncogene function. Importantly, our analysis argues strongly against viral aetiology in several cancers where this has frequently been proposed. We provide a virus-tumour map of unprecedented scale that constitutes a reference for future studies of tumour-associated viruses using transcriptome sequencing data.