The quality of a learning-based Wi-Fi sensing system is bounded by the quantity and quality of training data. However, obtaining sufficient and high-quality data across different domains is difficult due to extensive user involvement. We present CARING, a federated-learning-based framework to support collaborative and cross-domain Wi-Fi sensing. A key challenge of CARING is to allow the effective exchange and learning of knowledge across local models that are derived from heterogeneous data sources with uneven data distributions. We overcome this challenge by first extracting the activity-related representation to train local models. The shared global model aggregates received local model parameters and sends them back to individual devices for fine-tuning locally in the deployed environment. By leveraging the crowdsourced knowledge, CARING allows local models to quickly adapt to domain changes using just a few samples seen at test time. We demonstrate the benefit of CARING by applying it to activity recognition across three public datasets collected from 5 environments, 7 deployments, 31 users, and 29 activities. Experimental results show that CARING is highly effective and robust, improving the alternative approach for using single-sourced training data by up to 47%, giving an accuracy of over 80% (up to 100%) for various cross-domain scenarios.