Mobile Edge Computing (MEC) pushes computing functionalities away from the centralized cloud to the network edge, thereby meeting the latency requirements of many emerging mobile applications and saving backhaul network bandwidth. Although many existing works have studied computation offloading policies, service caching is an equally, if not more important, design topic of MEC, yet receives much less attention. Service caching refers to caching application services and their related databases/libraries in the edge server (e.g. MEC-enabled BS), thereby enabling corresponding computation tasks to be executed. Because only a small number of application services can be cached in resource-limited edge server at the same time, which services to cache has to be judiciously decided to maximize the edge computing performance. In this paper, we investigate the extremely compelling but much less studied problem of dynamic service caching in MEC-enabled dense cellular networks. We propose an efficient online algorithm, called OREO, which jointly optimizes dynamic service caching and task offloading to address a number of key challenges in MEC systems, including service heterogeneity, unknown system dynamics, spatial demand coupling and decentralized coordination. Our algorithm is developed based on Lyapunov optimization and Gibbs sampling, works online without requiring future information, and achieves provable close-to-optimal performance. Simulation results show that our algorithm can effectively reduce computation latency for end users while keeping energy consumption low.