We propose methods for estimating the probability that an entity from an entity database is associated with a web search query. Association is modeled using a query entity click graph, blending general query click logs with vertical query click logs. Smoothing techniques are proposed to address the inherent data sparsity in such graphs, including interpolation using a query synonymy model. A large-scale empirical analysis of the smoothing techniques, over a 2-year click graph collected from a commercial search engine, shows significant reductions in modeling error. The association models are then applied to the task of recommending products to web queries, by annotating queries with products from a large catalog and then mining query-product associations through web search session analysis. Experimental analysis shows that our smoothing techniques improve coverage while keeping precision stable, and overall, that our top-performing model affects 9% of general web queries with 94% precision.