The general rule is that the focal length of your lens will determine your minimum shutter speed for handholding. The formula is 1/focal length.
For instance, with a 200mm lens, you'll want 1/200 or faster. I always round up the nearest full stop, so that would be 1/250. It all depends on how steady you are. Some people can shoot a 200mm lens at 1/60 and get away with it. I cannot. You might not be able to shoot at 200mm with anything slower than 1/500. You'll have to do some testing on your own.
Digital Matt´s rule of thumb is quite accurate for SLRs, which is why I asked what kind of camera you are using.
Other types can be a bit different...for example, range-finders may let you use slower shutter speeds. Some modern digital cameras have electronic stabilization systems, making it possible to shoot at extremely low shutter speeds.
Check out a few tips to steady your shots:
Brace your body against something
Feet slightly apart
Brace your arms with your body
Camera held firmly in contact with your face (eye at you viewfinder)
Hold your breath
Push the button slowly and gently (some say "squeeze")
If you don´t have a tripod or even a monopod, then get one (!)...in the meantime think about what is around you that you can improvise with...I like to use my beer glass for example!
Garbz, I am confused on this one. The focal length of the lens does not change putting it on a crop body. It is just a crop of the field of view of the lens. Because of that the physical magnification of shake will not be increased by the smaller sensor. Why would you need to correct the focal length for this issue. Maybe I'm missing something here.
Gryphon, if you print a full frame 4x6" and also print a crop of the same photo as 4x6", the crop will show more shake at the equivalent print size. The image is magnified. Now, if you print the cropped photo 1.6x smaller, then they would "appear" roughly the same in terms of visible shake.