The ability to automatically detect stuttering events in speech could help speech pathologists track an individual's fluency over time or help improve speech recognition systems for people with atypical speech patterns. Despite increasing interest in this area, existing public datasets are too small to build generalizable dysfluency detection systems and lack sufficient annotations. In this work, we introduce Stuttering Events in Podcasts (SEP-28k), a dataset containing over 28k clips labeled with five event types including blocks, prolongations, sound repetitions, word repetitions, and interjections. Audio comes from public podcasts largely consisting of people who stutter interviewing other people who stutter. We benchmark a set of acoustic models on SEP-28k and the public FluencyBank dataset and highlight how simply increasing the amount of training data improves relative detection performance by 28\% and 24\% F1 on each. Annotations from over 32k clips across both datasets will be publicly released.