Affordances provide a natural means for a robot to describe its agency as actions it can perform on objects. Further, affordances can enable robots to reason complicated, multi-step tasks that involve proper use of a diversity of objects. This paper proposes the concept of affordance wayfields for representing manipulation affordances as objective functions in configuration space. Affordance wayfields quantify how well a path, or sequence of motions, will accomplish an afforded action on an object. Paths that enact affordances can be located by performing a randomized form of gradient descent over affordance wayfields. Incorporating obstacles, or other constraints into wayfields allows our method to adaptively generate valid motions for executing afforded actions. We demonstrate that affordance wayfields can enable robots, such as the Michigan Progress Fetch mobile manipulator, to solve complex real-world tasks such as assembling a table, or loading and unloading objects from a storage chest.