Despite their success, large pre-trained multilingual models have not completely alleviated the need for labeled data, which is cumbersome to collect for all target languages. Zero-shot cross-lingual transfer is emerging as a practical solution: pre-trained models later fine-tuned on one transfer language exhibit surprising performance when tested on many target languages. English is the dominant source language for transfer, as reinforced by popular zero-shot benchmarks. However, this default choice has not been systematically vetted. In our study, we compare English against other transfer languages for fine-tuning, on two pre-trained multilingual models (mBERT and mT5) and multiple classification and question answering tasks. We find that other high-resource languages such as German and Russian often transfer more effectively, especially when the set of target languages is diverse or unknown a priori. Unexpectedly, this can be true even when the training sets were automatically translated from English. This finding can have immediate impact on multilingual zero-shot systems, and should inform future benchmark designs.