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Despite remarkable advancements in few-shot generalization in natural language processing, most models are developed and evaluated primarily in English. To establish a rigorous and equitable evaluation framework for 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. Using BUFFET, we perform thorough evaluations of ten 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. Strong multilingual pre-trained or instruction-tuned models such as BLOOM or ChatGPT often lag behind much smaller mT5-base models given the same number of few-shot samples, particularly in low-resource languages. Our analysis suggests avenues for future research in few-shot cross-lingual transfer.