Floods are among the most common and devastating natural hazards, imposing immense costs on our society and economy due to their disastrous consequences. Recent progress in weather prediction and spaceborne flood mapping demonstrated the feasibility of anticipating extreme events and reliably detecting their catastrophic effects afterwards. However, these efforts are rarely linked to one another and there is a critical lack of datasets and benchmarks to enable the direct forecasting of flood extent. To resolve this issue, we curate a novel dataset enabling a timely prediction of flood extent. Furthermore, we provide a representative evaluation of state-of-the-art methods, structured into two benchmark tracks for forecasting flood inundation maps i) in general and ii) focused on coastal regions. Altogether, our dataset and benchmark provide a comprehensive platform for evaluating flood forecasts, enabling future solutions for this critical challenge. Data, code \& models are shared at https://github.com/Multihuntr/GFF under a CC0 license.