Word Sense Disambiguation (WSD) systems automatically choose the intended meaning of a word in context. In this article we present a WSD algorithm based on random walks over large Lexical Knowledge Bases (LKB). We show that our algorithm performs better than other graph-based methods when run on a graph built from WordNet and eXtended WordNet. Our algorithm and LKB combination compares favorably to other knowledge-based approaches in the literature that use similar knowledge on a variety of English data sets and a data set on Spanish. We include a detailed analysis of the factors that affect the algorithm. The algorithm and the LKBs used are publicly available, and the results easily reproducible.