One of the first signs of a leak in your furnace is a damp spot on the floor nearby. The moisture could be a sign that your furnace is not leaking directly, but that the drainage system it is using has become clogged. If the water encounters dirt and dust on its way to the drain, the debris can gather as sediment and eventually start closing the drain off, causing the water to leak.
Furnaces are also subject to cracking over time. If the section of the furnace where water vapor condenses is cracked, then the water may escape and leak into other parts of the furnace. Water within the unit has the potential to ruin sensors, electrodes and wiring.
When water comes into contact with the heat exchange in your furnace, the mixture of heat and water is a dangerous combination. Exchangers, which pass heat through metal to different areas of the furnace, can also crack and warp. This leads not only to damage for the exchanger covering but also creates combustion and fire hazards for your furnace.
Your furnace may be connected to evaporators or humidifiers. These systems can also leak from their coils, causing water to drip down into the furnace. In summer, when air conditioners have to work hard, water may condense and leak through an evaporator. In winter, indoor coils may frost over; when the water melts, the same types of leakage can occur.