Mutational signatures are patterns of mutations that arise during tumorigenesis. We present an enhanced, practical framework for mutational signature analyses. Applying these methods on 3,107 whole genome sequenced (WGS) primary cancers of 21 organs reveals known signatures and nine previously undescribed rearrangement signatures. We highlight inter-organ variability of signatures and present a way of visualizing that diversity, reinforcing our findings in an independent analysis of 3,096 WGS metastatic cancers. Signatures with a high level of genomic instability are dependent on TP53 dysregulation. We illustrate how uncertainty in mutational signature identification and assignment to samples affects tumor classification, reinforcing that using multiple orthogonal mutational signature data is not only beneficial, it is essential for accurate tumor stratification. Finally, we present a reference web-based tool for cancer and experimentally-generated mutational signatures, called Signal (https://signal.mutationalsignatures.com), that also supports performing mutational signature analyses.