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Large reasoning models have demonstrated remarkable proficiency in various tasks. However, we observe that they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning, leading to incorrect conclusions. This behavior presents significant challenges, not only in reasoning-intensive domains but also in realistic settings. To systematically investigate reasoning rigidity, a behavior unexplored in prior work, we introduce a dataset, ReasoningTrap, consisting of math problems, puzzles, and agentic tasks designed to diagnose reasoning rigidity. Using this dataset, we identify patterns that occur when models default to ingrained reasoning, and suggest inference-level and GRPO-based post-training remedies. Our diagnostic set and evaluation code are available at the project page to facilitate future research on mitigating reasoning rigidity in language models.