Self-driving cars and trucks, autonomous vehicles (AVs), should not be accepted by regulatory bodies and the public until they have much higher confidence in their safety and reliability -- which can most practically and convincingly be achieved by testing. But existing testing methods are inadequate for checking the end-to-end behaviors of AV controllers against complex, real-world corner cases involving interactions with multiple independent agents such as pedestrians and human-driven vehicles. While test-driving AVs on streets and highways fails to capture many rare events, existing simulation-based testing methods mainly focus on simple scenarios and do not scale well for complex driving situations that require sophisticated awareness of the surroundings. To address these limitations, we propose a new fuzz testing technique, called AutoFuzz, which can leverage widely-used AV simulators API grammars. to generate semantically and temporally valid complex driving scenarios (sequences of scenes). AutoFuzz is guided by a constrained Neural Network (NN) evolutionary search over the API grammar to generate scenarios seeking to find unique traffic violations. Evaluation of our prototype on one state-of-the-art learning-based controller and two rule-based controllers shows that AutoFuzz efficiently finds hundreds of realistic traffic violations resembling real-world crashes. Further, fine-tuning the learning-based controller with the traffic violations found by AutoFuzz successfully reduced the traffic violations found in the new version of the AV controller software.