They certainly do! Dogs in particular seem to have a sixth sense about people (good and bad) and about impending storms. They also know when to be gentle, with a baby for example.
Birds stop singing when a storm is on the way and then sing their little hearts out when the sun shines through once more.
We have too much distracting us to be so attentive to the world around us, which is a shame. Maybe if we woke up and smelt the roses the world would be a better place (before there are no more roses to smell).