Deep learning allows for accelerated magnetic resonance image (MRI) reconstruction, thereby shortening measurement times. Rather than using sparsifying transforms, a prerequisite in Compressed Sensing (CS), suitable MRI prior distributions are learned from data. In clinical practice, both the underlying anatomy as well as image acquisition settings vary. For this reason, deep neural networks must be able to reapply what they learn across different measurement conditions. We propose to use Recurrent Inference Machines (RIM) as a framework for accelerated MRI reconstruction. RIMs solve inverse problems in an iterative and recurrent inference procedure by repeatedly reassessing the state of their reconstruction, and subsequently making incremental adjustments to it in accordance with the forward model of accelerated MRI. RIMs learn the inferential process of reconstructing a given signal, which, in combination with the use of internal states as part of their recurrent architecture, makes them less dependent on learning the features pertaining to the source of the signal itself. This gives RIMs a low tendency to overfit, and a high capacity to generalize to unseen types of data. We demonstrate this ability with respect to anatomy by reconstructing brain and knee scans, as well as other MRI acquisition settings, by reconstructing scans of different contrast and resolution, at different field strength, subjected to varying acceleration levels. We show that RIMs outperform CS not only with respect to quality metrics, but also according to a rating given by an experienced neuroradiologist in a double blinded experiment. Finally, we show with qualitative results that our model can be applied to prospectively under-sampled raw data, as acquired by pre-installed acquisition protocols.