I used to think a high sync speed was useful only for underexposing the ambient or eliminating it completely. However, even if you have no interest in totally killing ambient, a high sync speed can be useful for effectively multiplying your flash power.
A SIMPLE TEST
Here is a series of test shots to demonstrate this concept. (For these test shots, I used a Nikon D70 which has a "natural" sync speed of 1/500, which is twice as fast as the 1/250 sync speed of many other cameras.)
If you compare these two shots (with bounce flash), the overall exposure looks similar, and the flash/ambient balance is similar.
However, the second shot needed only half as much light from the flash, compared to the first shot, thanks to a higher sync speed.
First, to show the amount of ambient light, I took an all-ambient shot. The exposure was ISO 200, f/2.8, 1/30.
I then took a baseline shot with bounce flash (TTL, with the flash pointed to camera rear right). I set shutter speed to the usual sync speed of 1/250, and underexposed ambient by about 1 stop. The resulting exposure was ISO 640, f/2.8, 1/250. TTL then added just enough flash to result in a normal exposure (not underexposure).
I took another test shot, this time using a higher sync speed of 1/500. Again underexposing ambient by 1 stop, the resulting exposure was ISO 1600, f/2.8, 1/500. TTL again added enough flash to result in a normal exposure (not underexposure).
Comparing the exposure of the baseline shot with the test shot, the flash had to work about twice as hard in the first shot (ISO 640, f/2.8) as in the second shot (ISO 1600, f/2.8). Thus, we were able to use a high sync speed not to underexpose the ambient, but to get a higher effective flash range.
WHAT ABOUT HIGH SPEED SYNC?
If being able to sync at high shutter speeds effectively increases flash power, what about using high speed sync? Recap: above a camera's sync speed, cameras with mechanical shutters use the front curtain and rear curtain to form a slit that travels across the sensor. See this slow-motion video of a shutter at 1/1000 speed:
At these speeeds, the sensor is never fully exposed at any given time, therefore if we use a flash, the flash would be partially blocked by the rear curtain, visible as a black bar across the frame.
High speed sync gets around the sync speed limitation by emitting many bursts of flash over the entire time period that the sensor is exposed by the moving slit.
The problem with HSS is that it weakens your flash by at least 2 stops compared to using a neutral density filter. Moreover, the higher your shutter speed, the weaker the flash gets.
For my D300 (with a 1/250 natural sync speed), the indicated range of an SB-800 at ISO 200, f/2.8 is 20 meters at a shutter speed of 1/250 or slower. At 1/500 (1 stop faster), the range drops to 9.5 meters (a reduction of more than 2 stops).
At 1/1000, the range is 6.7m.
At 1/2000, the range is 4.8m.
At 1/4000, the range is 3.4m.
At 1/8000, the range is 2.4m.
In other words, any gain in flash efficiency from the use of a higher shutter speed is more than offset by the HSS penalty. HSS is a losing proposition in terms of power and efficiency, and it's not a substitute for a higher natural sync speed.