This paper highlights the importance of personalization in large language models and introduces the LaMP benchmark --- a novel benchmark for training and evaluating language models for producing personalized outputs. LaMP offers a comprehensive evaluation framework with diverse language tasks and multiple entries for each user profile. It consists of seven personalized tasks, spanning three text classification and four text generation tasks. We additionally propose two retrieval augmentation approaches that retrieve personal items from each user profile for personalizing language model outputs. To this aim, we study various retrieval models, including term matching, semantic matching, and time-aware methods. Extensive experiments on LaMP for zero-shot and fine-tuned language models demonstrate the efficacy of the proposed retrieval augmentation approach and highlight the impact of personalization in various natural language tasks.