I've been fortunate enough to purchase a '97 328I with 68,000 miles in great condition.
However, late in the night--anywhere between 11pm-7am--the alarm goes off for no visible or audible reason. I've actually been outside near the car and heard the car alarm go off.
While the stock BMW alarm is music to my ears, my neighbors don't share my taste. I've since left the alarm off while parked at home.
I called the dealer I purchased the vehicle from, and his response was a possible wearing out of a sensor either in the dash or headliner. Though given that this is a used vehicle, he isn't offering to fix it without compensation.