Generalization performance is a key metric in evaluating machine learning models when applied to real-world applications. Good generalization indicates the model can predict unseen data correctly when trained under a limited number of data. Federated learning (FL), which has emerged as a popular distributed learning framework, allows multiple devices or clients to train a shared model without violating privacy requirements. While the existing literature has studied extensively the generalization performances of centralized machine learning algorithms, similar analysis in the federated settings is either absent or with very restrictive assumptions on the loss functions. In this paper, we aim to analyze the generalization performances of federated learning by means of algorithmic stability, which measures the change of the output model of an algorithm when perturbing one data point. Three widely-used algorithms are studied, including FedAvg, SCAFFOLD, and FedProx, under convex and non-convex loss functions. Our analysis shows that the generalization performances of models trained by these three algorithms are closely related to the heterogeneity of clients' datasets as well as the convergence behaviors of the algorithms. Particularly, in the i.i.d. setting, our results recover the classical results of stochastic gradient descent (SGD).