Large Language Models (LLMs) are increasingly used not only to generate code, but also to judge it: comparing, ranking, or scoring competing solutions. However, their reliability in this evaluative role remains poorly understood. Inconsistent or flawed judgments can undermine benchmarks and distort training signals. This paper investigates the performance and robustness of LLMs when used as code judges. We introduce CodeJudgeBench, a benchmark explicitly designed to evaluate LLM-as-a-Judge models across three critical coding tasks: code generation, code repair, and unit test generation. We comprehensively benchmark the performance of 26 LLM-as-a-Judge models, encompassing general-purpose, code-tuned, and reasoning models. Our empirical findings reveal that relatively small reasoning models (e.g., Qwen3-8B) can outperform much larger non-reasoning models up to 70B. We further stress-test robustness by applying both general and code-specific perturbations. All models show significant instability and are sensitive to changes such as response ordering, variable naming, and misleading comments. These findings highlight serious concerns about the consistency and robustness of LLM-based judges for coding tasks.