Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addresses the active localization problem for each. The robot, whose configuration is composed of its position and orientation, moves in a fully-known, simply connected polygonal environment. We pose the localization task as a planning problem in the robot's information space, which encapsulates the uncertainty in the robot's configuration. We consider robots equipped with: 1) angular and linear odometers; 2) a compass and contact sensor and; 3) an angular odometer and contact sensor. We present localization algorithms for models 1 and 2 and show that no algorithm exists for model 3. An implementation with simulation examples is presented.