Learning representations that accurately model semantics is an important goal of natural language processing research. Many semantic phenomena depend on syntactic structure. Recent work examines the extent to which state-of-the-art models for pre-training representations, such as BERT, capture such structure-dependent phenomena, but is largely restricted to one phenomenon in English: number agreement between subjects and verbs. We evaluate BERT's sensitivity to four types of structure-dependent agreement relations in a new semi-automatically curated dataset across 26 languages. We show that both the single-language and multilingual BERT models capture syntax-sensitive agreement patterns well in general, but we also highlight the specific linguistic contexts in which their performance degrades.