The act of encountering information unexpectedly has long been identified as valuable, both as a joy in itself and as part of task-focused problem solving. There has been a concern that highly accurate search engines and targeted personalization may reduce opportunities for serendipity on the Web. We examine whether there is the potential for serendipitous encounters during Web search, and whether improving search relevance through personalization reduces this potential. By studying Web search query logs and the results people judge relevant and interesting, we find many of the queries people perform return interesting (potentially serendipitous) results that are not directly relevant. Rather than harming serendipity, personalization appears to identify interesting results in addition to relevant ones.