Serverless computing offers a scalable event-based paradigm for deploying managed cloud-native applications. Function triggers are essential building blocks in serverless, as they initiate any function execution. However, function triggering is insufficiently studied and inherently hard to measure given the distributed, ephemeral, and asynchronous nature of event-based function coordination. To address this gap, we present TriggerBench, a cross-provider benchmark for evaluating serverless function triggers based on distributed tracing. We evaluate the trigger latency (i.e., time to transition between two functions) of eight types of triggers in Microsoft Azure and three in AWS. Our results show that all triggers suffer from long tail latency, storage triggers introduce variable multi-second delays, and HTTP triggers are most suitable for interactive applications. Our insights can guide developers in choosing optimal event or messaging triggers for latency-sensitive applications. Researchers can extend TriggerBench to study the latency, scalability, and reliability of further trigger types and cloud providers.