CyberGreg; You have two alarms, remember the one on the dash in case someone trys to jack up your car to steel your tires or tow it away. Of course you have the regular alarm also. The alarm even has its own rechargeable battery pack so disconnecting your battery does not disable it.
Once the alarm is on, it is triggered if you: 1. open the doors, hood or hatch 2. try to remove the radio 3. jump the ignition 4. open the glove box

English_Bob,
If everything was working right and you set your tow away alarm, before you left the car, then someone could have set it off by leaning on your car.