How can I monitor my roof to detect roof leaks before they cause damage?

A lot of questions have been asked about how to locate a leak in a roof, but you can only locate a leak that you know exists, and the first noticeable sign that there is anything wrong might be drywall damage in your living space.

By this point, the drywall is obviously already damaged, and the roof decking or other behind-the-scenes parts of the house might also have significant damage, so you need to pay not only to repair the leak but to clean up the damage it caused.

If you knew about the leak when it first started, you might be able to repair the leak early enough that it wouldn't have time to damage anything else.

How can you monitor or screen for leaks or possible leak-causing damage in a residential roof, so that they can be fixed before they cause water damage?