An off camera light or flash is a necessity during most weddings (especially indoor weddings). We prefer shooting with natural light but sometimes that is not enough. Even shooting family formals outside in the sun can leave harsh shadows on the face which need to be filled with another light source. An on camera flash (even with a plastic stofen diffuser) can sometimes be too harsh and look too much like an obvious flash. When we need more light we use an off camera flash with a softbox to achieve a more natural looking photograph.
Our off camera lighting setup is pretty simple: Canon 580 EX II speedlite, Rogue Flashbender w/ Diffusion panel, Phottix Strato II trigger, and a tripod or monopod (if an assistant holds the setup). We also hook up an external battery pack to our speedlite to get faster refresh times. The Rogue Flashbender adds a nice softbox like diffusion to the light casting a nice fill.
Best times to use an off camera flash during a wedding are family formal portraits, first toasts, and first dances.