Although numerous devices exist to track and share exercise routines based on running and walking, these devices offer limited functionality for strength-training exercises. We introduce RecoFit, a system for automatically tracking repetitive exercises - such as weight training and calisthenics - via an arm-worn inertial sensor. Our goal is to provide real-time and post-workout feedback, with no user-specific training and no intervention during a workout. Toward this end, we address three challenges: (1) segmenting exercise from intermittent non-exercise periods, (2) recognizing which exercise is being performed, and (3) counting repetitions. We present cross-validation results on our training data and results from a study assessing the final system, totaling 114 participants over 146 sessions. We achieve precision and recall greater than 95% in identifying exercise periods, recognition of 99%, 98%, and 96% on circuits of 4, 7, and 13 exercises respectively, and counting that is accurate to ±1 repetition 93% of the time. These results suggest that our approach enables a new category of fitness tracking devices.