Decay and rot are used to describe decomposing organic material. Corrode is usually used to describe materials, especially metals, being damaged by chemical actions.

To add to Jack's answer, I would say "rot" is normally used when talking about wood.

They all have the basic meaning of 'to break down', but each one refers to a different substance. When I hear 'corrode' I think of metal. When metal becomes rusty, it has corroded. Decay is usually talking about a living thing that has died. When a plant or animal dies, it starts to decay. Rot is basically the same as decay, and I can't really think of any situations in which you could use one but not the other.