Recent years have witnessed a rapid growth in the mass adoption of vehicle sharing systems across the world. Among various vehicle sharing systems, electric vehicle (EV) sharing is considered as the most effective means in reducing fossil fuel consumption and alleviating urban transportation problems. In this paper, we study how to further enhance the effectiveness of EV sharing as a promising sustainable transportation solution for the future by integrating vehicle-to-grid (V2G) electricity selling in EV sharing systems. In specific, we study service-zone and facility capacity planning and fleet management in EV sharing systems with V2G integration. We formulate the problem as a two-stage stochastic integer program. In the first stage, we optimize integer decision variables representing the planning of service zones, the capacity of parking and charging facilities, and the allocation of EVs in each zone under uncertain time-dependent travel demand and electricity prices. In the second stage, for each demand-price realization, we construct a time-and-vehicle-charging-status-expanded transportation network and optimize the operations of shared vehicle fleet, the charging of EV batteries, and the V2G selling process. We develop Benders decomposition and scenario decomposition algorithms for efficiently solving the proposed models with finite samples. By solving diverse instances generated from real-world and synthetic data, we demonstrate the computational efficacy of our approaches and study the benefits of integrating V2G in EV sharing from three aspects, including i) service provider benefit through higher profitability, ii) consumer benefit through improved service satisfaction, and iii) socio-environmental benefit through the reduction of private vehicle ownership and mileage and providing flexible capacity to the power grid.