While recent audio-visual models have demonstrated impressive performance, their robustness to distributional shifts at test-time remains not fully understood. Existing robustness benchmarks mainly focus on single modalities, making them insufficient for thoroughly assessing the robustness of audio-visual models. Motivated by real-world scenarios where shifts can occur $\textit{simultaneously}$ in both audio and visual modalities, we introduce $\texttt{AVROBUSTBENCH}$, a comprehensive benchmark designed to evaluate the test-time robustness of audio-visual recognition models. $\texttt{AVROBUSTBENCH}$ comprises four audio-visual benchmark datasets, $\texttt{AUDIOSET-2C}$, $\texttt{VGGSOUND-2C}$, $\texttt{KINETICS-2C}$, and $\texttt{EPICKITCHENS-2C}$, each incorporating 75 bimodal audio-visual corruptions that are $\textit{co-occurring}$ and $\textit{correlated}$. Through extensive evaluations, we observe that state-of-the-art supervised and self-supervised audio-visual models exhibit declining robustness as corruption severity increases. Furthermore, online test-time adaptation (TTA) methods, on $\texttt{VGGSOUND-2C}$ and $\texttt{KINETICS-2C}$, offer minimal improvements in performance under bimodal corruptions. We further propose $\texttt{AV2C}$, a simple TTA approach enabling on-the-fly cross-modal fusion by penalizing high-entropy samples, which achieves improvements on $\texttt{VGGSOUND-2C}$. We hope that $\texttt{AVROBUSTBENCH}$ will steer the development of more effective and robust audio-visual TTA approaches. Our code is available $\href{https://github.com/sarthaxxxxx/AV-C-Robustness-Benchmark}{here}$.