Intelligent Transportation Systems (ITS) aim at integrating sensing, control, analysis, and communication technologies into travel infrastructure and transportation to improve mobility, comfort, safety, and efficiency. Car manufacturers are continuously creating smarter vehicles, and advancements in roadways and infrastructure are changing the feel of travel. Traveling is becoming more efficient and reliable with a range of novel technologies, and research and development in ITS. Safer vehicles are introduced every year with greater considerations for passenger and pedestrian safety, nevertheless, the new technology and increasing connectivity in ITS present unique attack vectors for malicious actors. Smart cities with connected public transportation systems introduce new privacy concerns with the data collected about passengers and their travel habits. In this paper, we provide a comprehensive classification of security and privacy vulnerabilities in ITS. Furthermore, we discuss challenges in addressing security and privacy issues in ITS and contemplate potential mitigation techniques. Finally, we highlight future research directions to make ITS more safe, secure, and privacy-preserving.