A general framework for the verification of probabilistic forecasts of multivariate quantities is introduced. We propose tools for the assessment of calibration and sharpness, including a multivariate analogue of the verification rank or Talagrand diagram, which we compare to the minimum spanning tree histogram. The energy score is a proper scoring rule that applies to forecasts of vector-valued quantities and generalizes the continuous ranked probability score. It is expressed in the same unit as the observed variable and provides a direct way of comparing various deterministic and probabilistic forecasts using a single metric. An application to the University of Washington mesoscale ensemble points at strengths and deficiencies of probabilistic short-range forecasts of surface wind vectors, and allows us to assess opportunities and challenges in statistical postprocessing.