Several apartment management publications identify the roof as the most frequent source of apartment ceiling leaks. Even a small fissure in a roof's covering or coating can let water trickle in, following a pipe or a beam to your ceiling.
A prolonged dry spell and leak-free spell suggests the roof as the source of your problems. Because of the area involved, tracing and stopping roof leaks can take more than one try.
Other Exterior Issues
Suspect non-roof water issues if leaks tend to appear mostly on exterior walls and ceiling edges. Clogged drains are a frequent problem, as are damaged gutters.
Brick or stone buildings need small cracks or missing chunks of mortar replaced, commonly called repointing, on a regular basis to prevent ceiling and wall leaks.
Indoor Leakage Causes
Not only indoor plumbing, but water pipes, seals and tiling can be the source of leaks from one apartment to another. Shower piping may be solid, but tile grout needs replacing.
Small, persistent leaks may travel some distance from above, running along beams or pipes before dripping down, so cannot always be ascribed to the apartment directly above the leak. Tenants should therefore be accommodating to plumbing inspections even if the ceilings of the apartment below are dry.
Massive leaks caused by other tenants probably happen on television more than in real life. Assume, when contacting overhead tenants about leaks, that they are as careful and respectful of property as you are, unless you have definite evidence to the contrary.
Leaks can come from enough sources that creating friction with neighbors is unnecessary.