One safety concern of language models (LMs) is the reproduction of copyright-protected content, which raises questions of safety in terms of potential legal risk. Evaluating the degree of reproduction of copyright-protected content in LM generation is critical. Although both literal and non-literal similarities are considered by courts when assessing the degree of reproduction, prior research has focused only on literal similarities. To bridge this gap, we introduce CopyBench, a benchmark designed to measure both literal and non-literal copying in LM generations. Using copyrighted fiction books as text sources, we provide automatic evaluation protocols to assess literal and non-literal copying, balanced against the model utility in terms of the ability to recall facts from the copyrighted works and generate fluent completions. We find that, although literal copying is relatively rare, two types of non-literal copying---event copying and character copying---occur even in models as small as 7B parameters. Larger models demonstrate significantly more copying, with literal copying rates increasing from 0.2\% to 10.5\% and non-literal copying from 2.3\% to 5.9\% when comparing Llama3-8B and 70B models, respectively. We further evaluate the effectiveness of current strategies for mitigating copying and show that (1) training-time alignment can reduce literal copying but may increase non-literal copying, and (2) current inference-time mitigation methods primarily reduce literal but not non-literal copying. We open source our prompts and code to support red-teaming efforts in the future development of language models.