Registering an object with respect to a robot's coordinate system is essential to industrial assembly tasks such as grasping and insertion. Touch-based registration algorithms use a probe attached to a robot to measure the positions of contact, then use these measurements to register the robot to a model of the object. In existing work on touch-based registration, the selection of contact positions is not typically addressed. We present an algorithm for selecting the next robot motion to maximize the expected information obtained by the resulting contact with the object. Our method performs 6-DOF registration in a Rao-Blackwellized particle filtering (RBPF) framework. Using the 3D model of the object and the current RBPF distribution, we compute the expected information gain from a proposed robot motion by estimating the expected entropy that the RBPF distribution would have as a result of being updated by the proposed motion. The motion that provides the maximum information gain is selected and used for the next measurement, and the process is repeated. We compare various methods for estimating entropy, including approximations based on kernel density estimation. We demonstrate entropy-based motion selection in fully automatic and human-guided registration, both in simulations and on a real robotic platform.