We present SpeechStew, a speech recognition model that is trained on a combination of various publicly available speech recognition datasets: AMI, Broadcast News, Common Voice, LibriSpeech, Switchboard/Fisher, Tedlium, and Wall Street Journal. SpeechStew simply mixes all of these datasets together, without any special re-weighting or re-balancing of the datasets. SpeechStew achieves SoTA or near SoTA results across a variety of tasks, without the use of an external language model. Our results include 9.0\% WER on AMI-IHM, 4.7\% WER on Switchboard, 8.3\% WER on CallHome, and 1.3\% on WSJ, which significantly outperforms prior work with strong external language models. We also demonstrate that SpeechStew learns powerful transfer learning representations. We fine-tune SpeechStew on a noisy low resource speech dataset, CHiME-6. We achieve 38.9\% WER without a language model, which compares to 38.6\% WER to a strong HMM baseline with a language model.