Building robust deep learning-based models requires large quantities of diverse training data. In this study, we investigate the use of federated learning (FL) to build medical imaging classification models in a real-world collaborative setting. Seven clinical institutions from across the world joined this FL effort to train a model for breast density classification based on Breast Imaging, Reporting & Data System (BI-RADS). We show that despite substantial differences among the datasets from all sites (mammography system, class distribution, and data set size) and without centralizing data, we can successfully train AI models in federation. The results show that models trained using FL perform 6.3% on average better than their counterparts trained on an institute's local data alone. Furthermore, we show a 45.8% relative improvement in the models' generalizability when evaluated on the other participating sites' testing data.