In this paper, we explore zero- and few-shot generalization for fact verification (FV), which aims to generalize the FV model trained on well-resourced domains (e.g., Wikipedia) to low-resourced domains that lack human annotations. To this end, we first construct a benchmark dataset collection which contains 11 FV datasets representing 6 domains. We conduct an empirical analysis of generalization across these FV datasets, finding that current models generalize poorly. Our analysis reveals that several factors affect generalization, including dataset size, length of evidence, and the type of claims. Finally, we show that two directions of work improve generalization: 1) incorporating domain knowledge via pretraining on specialized domains, and 2) automatically generating training data via claim generation.