Genome-wide association studies (GWASs) have recently revealed many genetic associations that are shared between different diseases. We propose a method, disPCA, for genome-wide characterization of shared and distinct risk factors between and within disease classes. It flips the conventional GWAS paradigm by analyzing the diseases themselves, across GWAS datasets, to explore their "shared pathogenetics". The method applies principal component analysis (PCA) to gene-level significance scores across all genes and across GWASs, thereby revealing shared pathogenetics between diseases in an unsupervised fashion. Importantly, it adjusts for potential sources of heterogeneity present between GWAS which can confound investigation of shared disease etiology. We applied disPCA to 31 GWASs, including autoimmune diseases, cancers, psychiatric disorders, and neurological disorders. The leading principal components separate these disease classes, as well as inflammatory bowel diseases from other autoimmune diseases. Generally, distinct diseases from the same class tend to be less separated, which is in line with their increased shared etiology. Enrichment analysis of genes contributing to leading principal components revealed pathways that are implicated in the immune system, while also pointing to pathways that have yet to be explored before in this context. Our results point to the potential of disPCA in going beyond epidemiological findings of the co-occurrence of distinct diseases, to highlighting novel genes and pathways that unsupervised learning suggest to be key players in the variability across diseases.