We propose a system that determines the salience of entities within web documents. Many recent advances in commercial search engines leverage the identification of entities in web pages. However, for many pages, only a small subset of entities are important, or central, to the document, which can lead to degraded relevance for entity triggered experiences. We address this problem by devising a system that scores each entity on a web page according to its centrality to the page content. We propose salience classification functions that incorporate various cues from document content, web search logs, and a large web graph. To cost-effectively train the models, we introduce a novel soft labeling methodology that generates a set of annotations based on user behaviors observed in web search logs. We evaluate several variations of our model via a large-scale empirical study conducted over a test set, which we release publicly to the research community. We demonstrate that our methods significantly outperform competitive baselines and the previous state of the art, while keeping the human annotation cost to a minimum.