If it only happens in rain and damp weather it is likely related to the ignition system. Moisture could be getting into something and shorting out the ignition system.
Simple culprits can include a cracked distributor cap, badly worn rotor (unlikely), worn or cracked plug wires. There are other items, but they get more complicated from there.
The cracks or problems with these parts can be hard to spot, the cracks can be invisible to the naked eye.
If it is still damp out, try taking the distributor cap off and spraying the inside of it with WD-40 (the WD stands for Water Displacer, and will remove the water), also try spraying the plug wires.
If it is dry out and the car is running normally, get a spray bottle filled with water, and spray the distributor cap, then spray the plug wires. If you spray something and the car starts chugging and stalling, that is likely the bad part and should be replaced.
If it has been a long time since the car's last tuneup, the simplest route may be to put new cap, rotor, and plug wires on it and see if that solves the issue.
Wet/damp spark plug wires could do that. Time for a new set.
car starts but shut off while driving
There is most likely something in the gas tank. When the car starts the fuel pump starts sucking in fuel and when the trash gets to it the gas will not be able to flow through the clogged pump so the car stalls. When it stalls the fuel pump stops suction and the trash comes out allowing it to start again.
vacuum leak
bad fuel pump, you dont have enough pressure to stay alive.
Probably an alternator.
Change the Coolant Temp sensor
Tune up
you need a new cam positioning sensor installed
What happens when the a/c is off, now. your alternator is bad or a bad/poor connection in the batt-alt-gnd circits. woody
When your car stalls when its raining, it may be getting water in the distributor cap. Make sure the cap is on properly.
Could be a clogged or partially clogged fuel filter, and/or the fuel pump itself. The asker doesn't say whether the car will restart immediately after is stalls or not.
The engine stops.