Recent advances in vision-language models (VLMs) trained on web-scale image-text pairs have enabled impressive zero-shot transfer across a diverse range of visual tasks. However, comprehensive and independent evaluation beyond standard benchmarks is essential to understand their robustness, limitations, and real-world applicability. This paper presents a systematic evaluation framework for VLMs under natural adversarial scenarios for diverse downstream tasks, which has been overlooked in previous evaluation works. We evaluate a wide range of VLMs (CLIP, robust CLIP, BLIP2, and SigLIP2) on curated adversarial datasets (typographic attacks, ImageNet-A, and natural language-induced adversarial examples). We measure the natural adversarial performance of selected VLMs for zero-shot image classification, semantic segmentation, and visual question answering. Our analysis reveals that robust CLIP models can amplify natural adversarial vulnerabilities, and CLIP models significantly reduce performance for natural language-induced adversarial examples. Additionally, we provide interpretable analyses to identify failure modes. We hope our findings inspire future research in robust and fair multimodal pattern recognition.