In our living room, the ceiling fan has four light bulbs, and we need to replace them at least every 4 weeks or so. They are 40 watt, 120 volt lights. They always blow out when they are NOT on. I've heard it quite a few times - during the day when we don't need the light on, you can hear the distinctive 'tink' sound that a bulb makes when blowing out, and sure enough, next time we turn the lights on, one has blown out.

I'm not sure what to make of it, and am concerned that there is something wrong with the wiring and that it could be a fire hazard. We recently had our heat pump motor blow out and start a fire in our crawl space, so I'm kind of a nervous nelly about fires right now. If anyone has any ideas, I'd appreciate it! Thanks.

I don't know what causes it, but I had the same problem. In October of 2006 I put in the energy saving fluorescent bulbs, and have not had a problem with it since.

Entirely possible, that the store your getting your bulbs from has a bad lot.

The only things I know of that cause bulbs to blow are, defective product, has been used its average life span, over voltage, heat and vibration.
The implication is that this has happened repeatedly so defective product is unlikely.
If it had lasted its normal life span you would not be asking the question.
Over voltage is out because the switch is off.
Heat is out because the bulb is not burning when it blows.
That leaves vibration. Some types of candelabrum bulbs seem to quite sensitive.
What's above the ceiling The tink you hear is the filament breaking This most often happens when the bulb is hot. Very unusual to break when cold unless dropped or mistreated.
Don't see a fire hazard because switch is off.

Loose neutral can cause high voltage, should be corrected if a problem.
130 volt Rough Service bulbs can provide more life than standard.
Is this during times it is Very cold?
Bad batch or cheap bulbs or vibration

It sounds like you have a problem in your supply or house wiring that is causing things to blow. Have you spoken to an electrician AND the power company?

It is very unlikely a bulb will blow with power not applied. It is much more likely that it blows AS power is being applied.