The swimming of Escherichia coli is powered by its multiple flagellar motors. Each motor spins either clockwise or counterclockwise, under the control of an intracellular regulator, CheY-P. There can be two mechanisms (extrinsic and intrinsic) to coordinate the switching of bacterial motors. The extrinsic one arises from the fact that different motors in the same cell sense a common input (CheY-P) which fluctuates near the motors' response threshold. An alternative, intrinsic mechanism is direct motor-motor coupling which makes synchronized switching energetically favorable. Here, we develop simple models for both mechanisms and uncover their different hallmarks. A quantitative comparison to the recent experiments suggests that the direct coupling mechanism may be accountable for the observed sharp correlation between motors in a single Escherichia coli. Possible origins of this coupling (e.g., hydrodynamic interaction) are discussed.