Depends on your camera quite a bit---and how the flash is triggered.
Some cameras, like the Nikon D40, can only shoot flash exposures up to 1/500 second when the flash is in the shoe, or using the built-in flash. But, when the flash is triggered via an adapter and a PC cord, the D40 can shoot flash exposures at up to 1/8000 second.
It's possible to fire some of the Alien Bees monolights or Comet or Dyna-Lite studio strobes at ridiculously high shutter speeds, while still getting a lot of flash power.
When you ask about your camera--you do know there are like 2,500 camera models in use,right?