I commonly shoot while walking. Stopping is often better if you can, but that isn't always practical.
Try for at least 1/(4x focal length equivalent), faster is better, slower and you will have motion blur in many shots, but it depends upon technique too.
Avoid rotating the camera in a rapid fashion, pan, skew or tilt will cause more blur than simply moving the camera forward while walking forward.
If you shoot towards (or away) from the direction you are moving, you can use a slower shutter speed than if you shoot sideways.
Be sure you don't bounce the camera around when you walk, imagine you're shooting video with it.