There is an increasing trend towards evaluating NLP models with LLMs instead of human judgments, raising questions about the validity of these evaluations, as well as their reproducibility in the case of proprietary models. We provide JUDGE-BENCH, an extensible collection of 20 NLP datasets with human annotations covering a broad range of evaluated properties and types of data, and comprehensively evaluate 11 current LLMs, covering both open-weight and proprietary models, for their ability to replicate the annotations. Our evaluations show substantial variance across models and datasets. Models are reliable evaluators on some tasks, but overall display substantial variability depending on the property being evaluated, the expertise level of the human judges, and whether the language is human or model-generated. We conclude that LLMs should be carefully validated against human judgments before being used as evaluators.