In the past few years, we have witnessed a rise in the popularity of ride-hailing services (RHSs), an on-line marketplace that enables accredited drivers to use their own cars to drive ride-hailing users. Unlike other transportation services, RHSs raise significant privacy concerns , as providers are able to track the precise mobility patterns of millions of riders worldwide. We present the first survey and analysis of the privacy threats in RHSs. Our analysis exposes high-risk privacy threats that do not occur in conventional taxi services. Therefore, we propose PrivateRide, a privacy-enhancing and practical solution that offers anonymity and location privacy for riders, and protects drivers' information from harvesting attacks. PrivateRide lowers the high-risk privacy threats in RHSs to a level that is at least as low as that of many taxi services. Using real data-sets from Uber and taxi rides, we show that PrivateRide significantly enhances riders' privacy, while preserving tangible accuracy in ride matching and fare calculation, with only negligible effects on convenience. Moreover, by using our Android implementation for experimental evaluations, we show that PrivateRide's overhead during ride setup is negligible. In short, we enable privacy-conscious riders to achieve levels of privacy that are not possible in current RHSs and even in some conventional taxi services, thereby offering a potential business differentiator.