I had a rash of flats on one bike some time back. The wheels on this bike took tubes with Schrader valves. The valve hole in the rim tape was just a wee little bit too small, and the valves on the tubes I was using were tapered. This would not allow the tube near the valve to fully seat against the rim. As a result of the tube not being supported by the rim near the valve, the tube would blow out right beside the valve. Sometimes it would take less than an hour, sometimes it would take up to two weeks, but the tube would always blow out and always right beside the valve. This never happened while the bike was being ridden, always while it was parked.

Since figuring out and correcting that problem I haven't had any further flats on that bike.