We study the problem of anticipating user search needs, based on their browsing activity. Given the current web page p that a user is visiting we want to recommend a small and diverse set of search queries that are relevant to the content of p, but also non-obvious and serendipitous. We introduce a novel method that is based on the content of the page visited, rather than on past browsing patterns as in previous literature. Our content-based approach can be used even for previously unseen pages. We represent the topics of a page by the set of Wikipedia entities extracted from it. To obtain useful query suggestions for these entities, we exploit a novel graph model that we call EQGraph (Entity-Query Graph), containing entities, queries, and transitions between entities, between queries, as well as from entities to queries. We perform Personalized PageRank computation on such a graph to expand the set of entities extracted from a page into a richer set of entities, and to associate these entities with relevant query suggestions. We develop an efficient implementation to deal with large graph instances and suggest queries from a large and diverse pool. We perform a user study that shows that our method produces relevant and interesting recommendations, and outperforms an alternative method based on reverse IR.