Inertial-sensor-based attitude estimation is a crucial technology in various applications, from human motion tracking to autonomous aerial and ground vehicles. Application scenarios differ in characteristics of the performed motion, presence of disturbances, and environmental conditions. Since state-of-the-art attitude estimators do not generalize well over these characteristics, their parameters must be tuned for the individual motion characteristics and circumstances. We propose RIANN, a ready-to-use, neural network-based, parameter-free, real-time-capable inertial attitude estimator, which generalizes well across different motion dynamics, environments, and sampling rates, without the need for application-specific adaptations. We gather six publicly available datasets of which we exploit two datasets for the method development and the training, and we use four datasets for evaluation of the trained estimator in three different test scenarios with varying practical relevance. Results show that RIANN outperforms state-of-the-art attitude estimation filters in the sense that it generalizes much better across a variety of motions and conditions in different applications, with different sensor hardware and different sampling frequencies. This is true even if the filters are tuned on each individual test dataset, whereas RIANN was trained on completely separate data and has never seen any of these test datasets. RIANN can be applied directly without adaptations or training and is therefore expected to enable plug-and-play solutions in numerous applications, especially when accuracy is crucial but no ground-truth data is available for tuning or when motion and disturbance characteristics are uncertain. We made RIANN publicly available.