Despite remarkable advancements in few-shot generalization in natural language processing, most models are developed and evaluated primarily in English. To facilitate research on few-shot cross-lingual transfer, we introduce a new benchmark, called BUFFET, which unifies 15 diverse tasks across 54 languages in a sequence-to-sequence format and provides a fixed set of few-shot examples and instructions. BUFFET is designed to establish a rigorous and equitable evaluation framework for few-shot cross-lingual transfer across a broad range of tasks and languages. Using BUFFET, we perform thorough evaluations of state-of-the-art multilingual large language models with different transfer methods, namely in-context learning and fine-tuning. Our findings reveal significant room for improvement in few-shot in-context cross-lingual transfer. In particular, ChatGPT with in-context learning often performs worse than much smaller mT5-base models fine-tuned on English task data and few-shot in-language examples. Our analysis suggests various avenues for future research in few-shot cross-lingual transfer, such as improved pretraining, understanding, and future evaluations.