The most aggravating was when I lived in an apartment and the two other apartments on my floor were empty. On night I began to hear the low-battery chirp of the alarm in one of the empty apartments. While the apartments were well insulated for sound, the chirp carries surprisingly far and well. I contacted the landlord the next day... nothing was done.. Apparently quality control on batteries is pretty tight, as the following night the other apartment's alarm started doing the same thing. Like a chorus of of electronic crickets or locusts. After about 4 days of this I got into the empty apartments (don't ask) and replaced the batteries myself.
The one in my kitchen, which has both photoelectric and ionization detectors in it, has the endearing quality of when the battery gets low, but not quite low enough to warn you, when you stumble downstairs in the groggy hours of the early morning and flip on the light, it will instantly start screaming from the light change. Not fun at 6AM.
A friend with a modern home has all the detectors linked wirelessly---if one starts screaming, they all scream. Unfortunately there's nothing to indicate which one cried wolf. In the wee hours of the morning, they all started screaming, causing pandemonium. After it was determined that no crisis occurred and batteries were replaced, everyone went back to bed... and awoke hours later to a repeat. Eventually the suspect device was found and replaced after several nights of this and the process of elimination.