I have 2 ceiling lights in one room that turn on with a single switch. One works fine every time. The other has blown 2 lightbulbs in 2 weeks (incandescent). There were CFL's in them earlier and I took them out to replace them with the incandescent type. The first one seemed to burn out after a short period. The second one's glass bulb (a week or so later) had literally broken apart, leaving the burned out filament exposed.

What's the possible problem, as these are fairly new fixtures but in an older house.

Thanks very much for your help.

I assume that the fixture are the same. What size bulb are you using? What is the maximum size bulb that the fixtures are rated for ?
Check the voltage at the fixture that is blowing bulbs. If voltage is 120V or less, switch the fixture that is blowing bulbs with the fixture that is not.