Pervasive computing applications commonly involve user's personal smartphones collecting data to influence application behavior. Applications are often backed by models that learn from the user's experiences to provide personalized and responsive behavior. While models are often pre-trained on massive datasets, federated learning has gained attention for its ability to train globally shared models on users' private data without requiring the users to share their data directly. However, federated learning requires devices to collaborate via a central server, under the assumption that all users desire to learn the same model. We define a new approach, opportunistic federated learning, in which individual devices belonging to different users seek to learn robust models that are personalized to their user's own experiences. However, instead of learning in isolation, these models opportunistically incorporate the learned experiences of other devices they encounter opportunistically. In this paper, we explore the feasibility and limits of such an approach, culminating in a framework that supports encounter-based pairwise collaborative learning. The use of our opportunistic encounter-based learning amplifies the performance of personalized learning while resisting overfitting to encountered data.