AI companionship, where users develop emotional bonds with AI systems, has emerged as a significant pattern with positive but also concerning implications. We introduce Interactions and Machine Attachment Benchmark (INTIMA), a benchmark for evaluating companionship behaviors in language models. Drawing from psychological theories and user data, we develop a taxonomy of 31 behaviors across four categories and 368 targeted prompts. Responses to these prompts are evaluated as companionship-reinforcing, boundary-maintaining, or neutral. Applying INTIMA to Gemma-3, Phi-4, o3-mini, and Claude-4 reveals that companionship-reinforcing behaviors remain much more common across all models, though we observe marked differences between models. Different commercial providers prioritize different categories within the more sensitive parts of the benchmark, which is concerning since both appropriate boundary-setting and emotional support matter for user well-being. These findings highlight the need for more consistent approaches to handling emotionally charged interactions.