Common causes of a car alarm sounding are a hood, trunk or door being opened, the car being jostled, or the window being broken. Different alarms are set up differently, so what sets off one alarm may not set off another alarm. Typically, more expensive alarms cover more eventualities.
Some of the above reasons leave physical evidence of tampering, such as open doors, trunks, hoods or broken windows. One common cause of mysterious car alarms is the car's battery dying. For many cars, the alarm system is powered by a hidden battery, and the alarm itself is programmed to go off if the main power source, the primary battery, is cut off. While this is intended to alert the car owner that someone has clipped the battery cables or done something else malicious, the battery dying on its own triggers this same response.
Another common cause of the car alarm going off is a false alarm due to the shock sensors. This is because various vibrations and shocks all close the circuit of the alarm the same way, resulting in it going off. This happens more often with older alarm systems. Newer alarm systems typically measure the severity of the shock, only sounding the alarm if the car is jostled severely.