1997 Mazda 626 A new but bad problem

I can be driving my car, and it runs just fine. But sometimes when I come to a complete stop, the car shakes vigorously and dies. It starts up and runs again. Also, if my car is sitting in park, it will run fine until I turn my lights on, or a/c or heater, then shakes and dies. It does not ALWAYS do this, just probably 7 times out of 10. I don't think it's my alternator, because it runs fine until I stop. What could be my problem? Thanks.