yup - equally important for nature photography, especially when you are using long lenses.
As a rule of thumb, the minimum shutter speed that you should use should be no slower than 1/focal-length, therefore, if you have a 80-200 (or 70-210) zoom lenses and you are shooting at 200/210mm setting, your shutter speed should be at 1/200s or faster.
Granted, if you have ultra-steady hands, you can get away with 1/125s or even 1/60s, but you WILL notice a vast difference if you were to compare a shot taken handheld at 1/60s vs a tripod-mounted shot at the same speed.