Personalized recommender systems have been criticized for limiting opportunities to consume diverse content and reinforcing self-bias leading to negative side effects on society. To address these issues, serendipity has emerged as a design goal of recommender systems increasing the long-term satisfaction of the users. However, research on serendipity in recommender systems has focused on improving the performance of algorithms to predict surprising and diverse items without considering the user’s desired experience. To investigate user expectations of serendipitous recommender systems, we conducted an eight-day diary study with eight participants, using the YouTube recommender system. We found that users expect serendipitous recommender systems not only to provide surprising and diverse items based on existing definitions of serendipity but also to guide the desired impact in the long-term perspectives and help them discover unrealized needs which do not rely on their past behaviors. Users also expect serendipitous recommender systems to provide items that could relieve their burden posed by novelty of serendipitous recommendations. Based on these findings, we discuss design implications for designing user-centered serendipitous recommender systems that can support users to experience fundamental values of serendipity.