During the operation of industrial robots, unusual events may endanger the safety of humans and the quality of production. When collecting data to detect such cases, it is not ensured that data from all potentially occurring errors is included as unforeseeable events may happen over time. Therefore, anomaly detection (AD) delivers a practical solution, using only normal data to learn to detect unusual events. We introduce a dataset that allows training and benchmarking of anomaly detection methods for robotic applications based on machine data which will be made publicly available to the research community. As a typical robot task the dataset includes a pick-and-place application which involves movement, actions of the end effector, and interactions with the objects of the environment. Since several of the contained anomalies are not task-specific but general, evaluations on our dataset are transferable to other robotics applications as well. In addition, we present multivariate time-series flow (MVT-Flow) as a new baseline method for anomaly detection: It relies on deep-learning-based density estimation with normalizing flows, tailored to the data domain by taking its structure into account for the architecture. Our evaluation shows that MVT-Flow outperforms baselines from previous work by a large margin of 6.2% in area under receiving operator characteristic.