When asked this question not a small percentage of photographers will take out their cameras, turn them to shutter priority, and spin the wheel to the end. This would give them usually 1/8000 and they would accordingly give that answer. And it's wrong. What if 1/8000 is not fast enough? What if you're trying to catch water flying through the air?
In this shot, I wanted the water really crisp. But to do that I need to shoot faster than a 1/8000. To make this happen, I need a 1/16000 of a second (actually, it ended up being faster.) How do you make that happen? You must light it. Doing so allows for a couple benefits. First, to get a 1/8000 in an ambient environment you must shoot at a ridiculous ISO and ruin the photo. Obviously that won't work. Second, you can achieve a faster effective shutter speed when you light. Here's why:
The period of time a flash actually creates light (called the flash duration) is a very short period of time, usually between 1/16000 and 1/32000 of a second. The lower the power output the faster the duration. Let us say you have set an ambient exposure triangle (ISO, f/stop, shutter) that gives you a totally black frame. No detail whatsoever. In the case above, that was 1/200, f/11, ISO 200. We were shooting in a garage and this exposure (without a flash) was a totally black frame.
That means that when a flash does fire it is the only light that will show up in the frame. It also means that the period of time that light actually exposes a subject is faster than the fastest shutter speed the camera can achieve on its own. And the lower you put the flash power output the faster it gets. I shot this at about 1/8 power, which means it's something like 1/32000 of a second, but we didn't check the manual of these particular flashes to be sure.
This is a simple shot to put together. Two flashes firing towards the camera. This is done so that no light hits the background. The flashes are in manual mode so that their duration does not change from shot to shot. It is important to note that the two flashes are the same model, so that their outputs (and thus, durations) are identical. The black background sits pretty far behind the table with the bowl on it (done so that water wont drench the background). We put food coloring in the water for some extra fun. Then old carpet or an old tarp or discolored towels below the table because we knew we would get water everywhere. We set the camera to manual focus and manual exposure. One person dropped berries from a ladder and the other person fired the camera. The trickiest part of the whole thing was trying to coordinate our respective jobs. I did this with my good friend Gary and I have to say it's a lot more fun and more successful done with a friend.
And thus, we have artificially expended our fastest shutter speed.