This paper introduces NorEval, a new and comprehensive evaluation suite for large-scale standardized benchmarking of Norwegian generative language models (LMs). NorEval consists of 24 high-quality human-created datasets -- of which five are created from scratch. In contrast to existing benchmarks for Norwegian, NorEval covers a broad spectrum of task categories targeting Norwegian language understanding and generation, establishes human baselines, and focuses on both of the official written standards of the Norwegian language: Bokmål and Nynorsk. All our datasets and a collection of over 100 human-written prompts are integrated into LM Evaluation Harness, ensuring flexible and reproducible evaluation. We describe the NorEval design and present the results of benchmarking 19 open-source pre-trained and instruction-tuned LMs for Norwegian in various scenarios. Our benchmark, evaluation framework, and annotation materials are publicly available.