The ice maker has a constant supply of water, so if the line supplying the water is damaged or loose, you are left with a constant leak. Locate the water inlet valve on the back of the refrigerator and make sure the connection is secure. Inspect the line itself for any sign of wear -- even something as innocuous as a bend or wrinkle can hide a tiny crack that allows water to escape.
The water line that feeds the ice maker also feeds the water dispenser, but the dispensers can also leak from the front. This can look like a leak from under the fridge as the water runs down the front surface and pools on the floor, or smaller leaks may pool on the dispenser platform. To tell the difference between spills and leaks, dry the platform and place a paper towel under both the water and ice chute. If the paper towel has water drops, there's a loose connection somewhere. Remove the dispenser panel and check for damaged lines or faulty connections.
The water that accumulates as a result of the automatic defrost system is supposed to funnel into a drain line that deposits it into the drain pan underneath the fridge. If the line is damaged, the outlet is clogged or the drain pan is overflowing or leaky, you may notice a sizable puddle underneath the fridge. Replacement drain pans are cheap and easy, but if the drain pan's okay, you must remove the service panel and manually remove any clogs in the line or outlet.
Refrigerator doors have light heaters inside to prevent the formation of condensation -- that's why the front of your fridge s not as cold as the inside, and never "weeps" moisture regardless of the temperature difference between the fridge and the room. If your fridge is set to Energy Saver mode, those door heaters are disabled to save on electricity. Switch to a regular mode and observe the unit for a day or so. If the leak continues, contact a repair person for further diagnosis.