Large Language Models (LLMs) have shown remarkable capabilities in various natural language processing tasks. However, LLMs may rely on dataset biases as shortcuts for prediction, which can significantly impair their robustness and generalization capabilities. This paper presents Shortcut Suite, a comprehensive test suite designed to evaluate the impact of shortcuts on LLMs' performance, incorporating six shortcut types, five evaluation metrics, and four prompting strategies. Our extensive experiments yield several key findings: 1) LLMs demonstrate varying reliance on shortcuts for downstream tasks, significantly impairing their performance. 2) Larger LLMs are more likely to utilize shortcuts under zero-shot and few-shot in-context learning prompts. 3) Chain-of-thought prompting notably reduces shortcut reliance and outperforms other prompting strategies, while few-shot prompts generally underperform compared to zero-shot prompts. 4) LLMs often exhibit overconfidence in their predictions, especially when dealing with datasets that contain shortcuts. 5) LLMs generally have a lower explanation quality in shortcut-laden datasets, with errors falling into three types: distraction, disguised comprehension, and logical fallacy. Our findings offer new insights for evaluating robustness and generalization in LLMs and suggest potential directions for mitigating the reliance on shortcuts. The code is available at \url {https://github.com/yyhappier/ShortcutSuite.git}.