We consider sensor data scheduling for remote state estimation. Due to constrained communication energy and bandwidth, a sensor needs to decide whether it should send the measurement to a remote estimator for further processing. We propose an event-based sensor data scheduler for linear systems and derive the corresponding minimum squared error estimator. By selecting an appropriate event-triggering threshold, we illustrate how to achieve a desired balance between the sensor-to-estimator communication rate and the estimation quality. Simulation examples are provided to demonstrate the theory.