State-of-the-art planners often exhibit substantial runtime variation, making it useful to be able to efficiently predict how long a given planner will take to run on a given instance. In other areas of AI, such needs are met by building so-called empirical performance models (EPMs), statistical models derived from sets of problem instances and performance observations. Historically, such models have been less accurate for predicting the running times of planners. A key hurdle has been a relative weakness in instance features for characterizing instances: mappings from problem instances to real numbers that serve as the starting point for learning an EPM. We propose a new, extensive set of instance features for planning, and investigate its effectiveness across a range of model families. We built EPMs for various prominent planning systems on several thousand benchmark problems from the planning literature and from IPC benchmark sets, and conclude that our models predict runtime much more accurately than the previous state of the art. We also study the relative importance of these features.