This simple and cheap moisture sensor can be use to close a switch that operates an alarm.
It operates on the principle that most ordinary paper is much stronger dry than wet. Ordinary copy paper has a tensile strength of about 17 times more when dry. A strip is glued to a wooden cloths pin, holding it open. It has to be mounted in such a way that it actuates a switch when it closes, simple enough?
Since it draws no current it is ideal for battery operated devices.
For a more advanced alarm it could be connected to a PIC that was programmed to give an initial alarm of 20 seconds and thereafter just a short one, every hour until battery dies or is disconnected.
Update. Fig.2 showes a much simpler version, the piece of cellulose sponge can be changed in seconds.