Large language models (LLMs) encode parametric knowledge about world facts and have shown remarkable performance in knowledge-driven NLP tasks. However, their reliance on parametric knowledge may cause them to overlook contextual cues, leading to incorrect predictions in context-sensitive NLP tasks (e.g., knowledge acquisition tasks). In this paper, we seek to assess and enhance LLMs' contextual faithfulness in two aspects: knowledge conflict and prediction with abstention. We demonstrate that LLMs' faithfulness can be significantly improved using carefully designed prompting strategies. In particular, we identify opinion-based prompts and counterfactual demonstrations as the most effective methods. Opinion-based prompts reframe the context as a narrator's statement and inquire about the narrator's opinions, while counterfactual demonstrations use instances containing false facts to improve faithfulness in knowledge conflict situations. Neither technique requires additional training. We conduct experiments on three datasets of two standard NLP tasks, machine reading comprehension and relation extraction, and the results demonstrate significant improvement in faithfulness to contexts. Code and data are released at https://github.com/wzhouad/context-faithful-llm.