Magnetic resonance (MR) fingerprinting is an emerging quantitative MR imaging technique that simultaneously acquires multiple tissue parameters in an efficient experiment. In this work, we present an estimation-theoretic framework to evaluate and design MR fingerprinting experiments. More specifically, we derive the Cramer-Rao bound (CRB), a lower bound on the covariance of any unbiased estimator, to characterize parameter estimation for MR fingerprinting. We then formulate an optimal experiment design problem based on the CRB to choose a set of acquisition parameters (e.g., flip angles and/or repetition times) that maximizes the signal-to-noise ratio efficiency of the resulting experiment. The utility of the proposed approach is validated by numerical studies. Representative results demonstrate that the optimized experiments allow for substantial reduction in the length of an MR fingerprinting acquisition, and substantial improvement in parameter estimation performance.