Recently large collections of swimming microorganisms have been observed producing collective motions on a scale much larger than the scale of a single organism. These motions could be important for phenomena such as swarming, biofilms, and infection by bacterial colonies. The motions may also be exploited in the design of new artificial self-propelled particles. To better understand the cause of these motions, simulations of large populations of hydrodynamically interacting swimming particles have been performed at low Reynolds number in periodic and confined geometries. We have examined how the hydrodynamic interactions lead to collective behavior of the organisms, and how this mechanism depends on the method of swimming. Some organisms push themselves from behind, while others pull themselves forward. Some organisms perform a "run-and-tumble" behavior to control motion towards or away from stimuli, while others are "smooth" swimmers. We will discuss the influence of these differences on the collective behavior. We will also discuss the impact of the collective behavior on probe particles which have been used to measure the microrheology of the suspension.