The next few years should see the birth of gravitational wave astrophysics, a revolutionary new way to learn about our Universe. Construction of advanced gravitational wave observatories, such as LIGO and Virgo, is actively underway. We focus on the most likely sources for these detectors, which is the inspiral and merger of a stellar mass binary system, such as a pair of neutron stars and/or black holes. In addition to being extraordinarily loud in gravitational waves, these systems may be associated with short gamma-ray bursts, and thus are also very bright in the electromagnetic spectrum. This offers the promise of multi-messenger astronomy: the combination of gravitational wave and electromagnetic observations to elucidate the physics and astrophysics of these sources. We present estimates for the event rate of these systems, showing that we can expect the first detections within months of operation. These measurements will teach us about the systems themselves (e.g., elucidating the central engine, constraining the beaming), as well as informing us about broad astrophysical and cosmological questions (e.g., the ratio of neutron stars to black holes, precision measurements of the Hubble constant). Of particular interest are the loudest events; we discuss the important role these have to play in gravitational wave astrophysics.