Genome-wide association studies (GWAS) are a powerful tool for understanding the genetic basis of diseases and traits, but most studies have been conducted in isolation, with a focus on either a single or a set of closely related phenotypes. We describe MetABF, a simple Bayesian framework for performing integrative meta-analysis across multiple GWAS using summary statistics. The approach is applicable across a wide range of study designs and can increase the power by 50% compared with standard frequentist tests when only a subset of studies have a true effect. We demonstrate its utility in a meta-analysis of 20 diverse GWAS which were part of the Wellcome Trust Case Control Consortium 2. The novelty of the approach is its ability to explore, and assess the evidence for a range of possible true patterns of association across studies in a computationally efficient framework.