It has been shown recently that the performance of greedy best-first search (GBFS) for computing plans that are not necessarily optimal can be improved by adding forms of exploration when reaching heuristic plateaus: from random walks to local GBFS searches. In this work, we address this problem but using structural exploration methods resulting from the ideas of width-based search. Width-based methodsseek novel states, are not goal oriented, and their power has been shown recently in the Atari and GVG-AI video-games. We show first that width-based exploration in GBFS is more effective than GBFS with local GBFS search (GBFS-LS), and then proceed to formulate a simple and general computational framework where standard goal-oriented search (exploitation) and width-based search (structural exploration) are combined to yield a search scheme, best-first width search, that is better than both and which results in classical planning algorithms that outperform the state-of-the-art planners.