Any information that must flow one way is useful through a write-only property. Generally we write classes for information to flow out of or in and out. In the case of write-only you have to think of situations where information should only flow in and not out. Usually this involves security type of information because we don't want a consumer to have any access in retrieving a secure piece of information. Passwords, CC numbers, etc...
When the information is not secure, e.g., when we don't mind anyone accessing it then we get the common get/set pattern. 99.9% of the time this is how properties are used. Since there are other ways, just as easy that can be more robust to achieve this, this is more of a semantic construct that was left in for symmetry than anything. One of the rare cases where something wasn't taken out and your left with "Why the heck did they remove that!".