Can most animals distinguish left from right?

In order to traverse a maze, I assume rats know left from right. Is this true of most mammals? If you hide food in your hand, could you train a dog to always choose the left or right hand? Animals are able to navigate over long distances. I read somewhere that they do not have maps in their heads, but use landmarks. Using a given landmark, do they distinguish left from right to know which way to turn? How far down the food chain do animals have this ability? Do reptiles and fish know left from right? What about worms and insects?