Camera speedlights are called speedlights because they are incredibly fast at lower power levels. Used at low power to stop extreme motion like water drop splashes or hummingbird wings. Here is a Nikon SB-800 speedlight duration chart from its manual:
1/1050 sec. at M1/1 Full output (t.5)
1/1100 sec. at M1/2 output
1/2700 sec. at M1/4 output
1/5900 sec. at M1/8 output
1/10900 sec. at M1/16 output
1/17800 sec. at M1/32 output
1/32300 sec. at M1/64 output
1/41600 sec. at M1/128 output
Yes, this would include freezing camera shake. Flash can be a big help for hand-held macro work.
And as mattdm pointed out, ambient light level should be dim (not dark, but certainly not bright) to prevent the continuous ambient light exposure from blurring the motion that the speedlight already stopped.
Full power is an exception measured to half power points called t.5, and the actual full power duration is more like 3x or 1/350 second. But the other levels are chopped off short to be low power, which makes them fast, and these numbers would be actual durations.
Note this is about camera speedlights. Studio monolights are typically voltage controlled, which work oppositely in a couple of ways, and their lowest power might be twice slower than their maximum power.
More info about it: http://www.scantips.com/speed.html