Could be a number of things.
The most likely possibilities are: (not in order of likelihood)
1. Heater core leak---pretty easy to diagnose since the coolant will feel sticky to the touch and will smell pretty badly. Solution: Replace heater core (big job).
2. AC evaporator drain is pluggged. As your AC cools the air, moisture is accumulated in a tray beneath the AC evaporater, under the dashboard. If the drain is plugged, instead of the moisture being channeled through the firewall to the outside of the car, it overflows into the passenger compartment. (Solution: remove appropriate under dash panels, access AC evaporator, the clear tray drain)
3. Clogged drains for fresh air vents. These vents are below your windshield wipers and take in fresh air for your AC/Heat system. If leaves or other organic matter get past the protective mesh on the vents, then when it rains, the water has no place to drain, since the drains get plugged by the debris. Slowly a little "fish tank" builds up in there, and once the water level gets high enough, it will seep through the fire wall past various grommets and wires that were never meant to be waterproof. (Solution: remove fresh air vent screens, take prop and unclog drains in the basin below).
4. Windshield leak. (Solution--reseal windshield).
5. Leak from door seals, window seals---inspect for damage, if there are door drains, unplug them.
6. Clogged sunroof drains. (Solution---open sun roof, blow compressed air into drains).