Deep learning approaches for tomographic image reconstruction have become very effective and have been demonstrated to be competitive in the field. Comparing these approaches is a challenging task as they rely to a great extent on the data and setup used for training. With the Low-Dose Parallel Beam (LoDoPaB)-CT dataset, we provide a comprehensive, open-access database of computed tomography images and simulated low photon count measurements. It is suitable for training and comparing deep learning methods as well as classical reconstruction approaches. The dataset contains over 40000 scan slices from around 800 patients selected from the LIDC/IDRI database. The data selection and simulation setup are described in detail, and the generating script is publicly accessible. In addition, we provide a Python library for simplified access to the dataset and an online reconstruction challenge. Furthermore, the dataset can also be used for transfer learning as well as sparse and limited-angle reconstruction scenarios.