There are many factors that can dictate how steady your hands are including the way you hold the camera, your level of experience, and even medical factors. In addition to this Image Stabilisation technology can compensate for hand movement too. However, in general a rule of thumb that is often advised for hand held photography where there is no Image Stabilisation being used is to use the reciprocal of the focal length as your shutter speed to avoid blurred pictures. At a focal length of 50mm you should use a shutter speed of 1/50s. At a focal length of 200mm you should use a faster shutter speed of 1/200s. This rule of thumb assumes your subject is not moving. If your subject is moving you need to increase your shutter speed to take account of the subjects movement if you want a photo without any motion blur.
This rule also assumes you are using a full frame camera (which I am not). Since my camera has a 1.6 crop sensor I need to multiply the focal length by 1.6 before reciprocating it for the required shutter speed. At 50mm I need to reciprocate 50 x 1.6 = 80 and therefore my shutter speed should be 1/80s (instead of 1/50s that you might assume if you don't take the crop in to account). At 200mm I need to reciprocate 200 x 1.6 = 320 and therefore my shutter speed should be 1/320s (instead of 1/200s that you might assume if you don't take the crop in to account). As you can see, the crop makes quite a bit of difference!
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