In this paper, we study downlink multi-user scheduling for a time-slotted system with simultaneous wireless information and power transfer. In particular, in each time slot, a single user is scheduled to receive information, while the remaining users opportunistically harvest the ambient radio frequency energy. We devise novel online scheduling schemes in which the tradeoff between the users' ergodic rates and their average amount of harvested energy can be controlled. In particular, we modify the well-known maximum signal-to-noise ratio (SNR) and maximum normalized-SNR (N-SNR) schedulers by scheduling the user whose SNR/N-SNR has a certain ascending order (selection order) rather than the maximum one. We refer to these new schemes as order-based SNR/N-SNR scheduling and show that the lower the selection order, the higher the average amount of harvested energy in the system at the expense of a reduced ergodic sum rate. The order-based N-SNR scheduling scheme provides proportional fairness among the users in terms of both the ergodic achievable rate and the average harvested energy. Furthermore, we propose an order-based equal throughput (ET) fair scheduler, which schedules the user having the minimum moving average throughput out of the users whose N-SNR orders fall into a given set of allowed orders. We show that this scheme provides the users with proportionally fair average harvested energies. In this context, we also derive feasibility conditions for achieving ET with the order-based ET scheduler. Using the theory of order statistics, the average per-user harvested energy and ergodic achievable rate of all proposed scheduling schemes are analyzed and obtained in closed form for independent and non-identically distributed Rayleigh, Ricean, Nakagami-m, and Weibull fading channels. Our closed-form analytical results are corroborated by simulations.