The movement of the subject will determine the shutter speed depending on the desired effect, but what should your minimum shutter speed be if the subject is static?
The 1/focal length is a good place to start, but that was thought up for 35mm film, so if you have a full frame sensor is still the place to start. Most people have crop sensor cameras though, where a 50mm lens gives the same view as a 75mm lens (80mm on Canon) on a FF camera. So for crop sensor cameras maybe it should 1/focal length x1.5 (or x1.6 for Canon).
As with all these 'rule of thumb' guides you need to check whether you can hold the camera steady or not at speeds approaching this 'rule of thumb' guide speed. And lenses with IS/VR may enable holding at slower shutter speeds. Camera technique also comes into play of course, and hold the camera at arms length using the LCD and all bet are off.
The only way to know though is to test you and your camera.