I've been having issues recently. Really weird ones.  First, it was my basement light. The bulb would not light when turned on, but if you tapped the fixture, it illuminated.   Now, my back porch light is doing the same thing. It doesn't come on when I turn the switch on, but if I tap the fixture, the bulb turns on and will be normal. This issue in the back porch light started yesterday. The issue with the basement light started in July.

I have 75W incandescent bulbs in both of them, made by Living Solutions (or is it Home Solutions?). They are cheap bulbs, yes.

I wired the back porch light myself in 2011, and I anchored down everything like Ft. Knox, tightened and taped the marettes tightly, and caulked around the light. So I know it's not an electrical fault with that one. But the basement fixture was done in the 1980's by my father & friends, and it's been half-crocked the way it is wired, and the electrical tape is drying out.

Which has me confused. Is it normal for bulbs to do this? Or is it the fixture itself?

Over the last 3 or 4 years, a couple of light bulbs, they actually broke at the screw and the base came unglued from the bulb, leaving me a perfectly intact bulb, which was also unusual.

It sounds like your problem is the bulbs. I've seen situations where a bulb will fail to light, then when you go to remove it, it lights. It seems to happen with the supported filaments most often. It is caused by the filament breaking in just one spot. When you touch the bulb, the vibration makes the filament ends touch and the bulb lights again. When the bulb is turned off and cools, the filament can separate again and you have to touch the bulb to get it to relight. This happened a lot with the Chinese Westinghouse 60 Watt bulbs used at work. It can get annoying.

I had similar behaviour, I first suspected the bulb as well. But the problem with unreliable light remained even after replacing the bulb: After that it worked for a while, but then the problems started again. But instead of replacing the bulb, virtually any manipulation with the bulb "solved" the problem for a while as well.
It took quite some time to find out, the problem was the socket design: The screw terminals were there riveted (you may see it on the left side, problematic is the center contact; this exact piece is from China, but the problem is shared among all sockets with that concept) to the contact springs. Normally, when inspecting without a bulb, everything looked tight. But the point was, it was tight just because of the "spring" action of the contacts when the bulb was not there. If you tighten the bulb, the pressure transfer ed to the bulb and the rivets connecting the screw terminals remain loose.
At first glance that rivet design looks very reliable: You just insert the wire into the hole of the brass terminal and tighten the screw from the side, way more reliable than if the screw thread is in the contact metal piece and you have to bend the wire around.

But when looking more carefully to the socket design and thinking about it, I realize with that socket concept it is actually impossible to make the rivet joints right. And I find out, that concept is almost universally used on most of the ceramic socket, even of different brands, they "share" the same error...

With the older design with the screw directly in the contact piece it was more fiddly to get the wire there, but once you "succeed", there was nothing else to make problems (at least of what my experience tells)

have you checked your lampholder?
It happened to me the same thing with semi-trailer, trailer and home and was the lampholder with an "little" space between live connection and lamp connection; i solved adding some soldering in the middle contact.

Hey there.  Just wanted to give everyone an update. Five days after this happened, after all the tapping to get it on, and it burning all night, the bulb finally burned out on Sunday evening (the 24th). There was a little tiny 1 or 2 millimeter long piece of filament coil broken off in the bulb.

Update again.  The brand new bulb I put in last night has come unglued from the base of the bulb and has broken within the lamp. I gotta get pliers in there and unscrew it. The filament and wires are all intact, the globe just dropped right off. That's the 3rd time that has happened since 2010 or so.

Isn't the socket overheatiing there? (base up, plastic socket, lamp wattage on maximum or close to maximum rating)
This usually leads to weakening of the cement there...
I have seen many fixtures with really inadequate ventilation arund the bulb...
Other cause could be water leak (and/or high humudity) inside of the fixture, the humidity, mainly followed by the heat tend to weaken the cements as well.

It is not normal to have these problems only with one or two fixtures...

The outside fixture is a porcelain socket, and I'm using 75's when it's rated for 60's, not that big of a difference. The maximum wattage rating is just there to protect the company from lawsuits because some dummy puts a 100W bulb in a 60W table lamp and the socket melts and catches the shade on fire. There is 3 more in the basement the exact same, and never have issues with them, and their bulbs last for 3 or 4 years. Those ones have plastic or brass sockets, I can't remember.

It's just cheap bulbs.  The bulbs are the $2.99-for-12 Home Luminaire bulbs. Sometimes the sockets are a bit loose out of the box to begin with, but I use them anyways and they work until they break.

There's no water leakage, but we have had cool nights and hot days lately.

The outside fixture is a porcelain socket, and I'm using 75's when it's rated for 60's, not that big of a difference.

That is quitesignificant difference, if normally the socket heats up to lets say 100degC with 30degC ambient, with the 25% higher wattage it means 120degC, so 20degCmore. And that is about 4x faster degradation ofmany materials, including the cement.

The maximum wattage rating is just there to protect the company from lawsuits because some dummy puts a 100W bulb in a 60W table lamp and the socket melts and catches the shade on fire.

That is not true. The lamps have some maximum allowed temperature ratings for both the bulb glass, as well as the socket.
And it is the fixture manufacturer responsibility to make sure the maximum wattage lamp he allows does not exceed these limits. And my experience tells, many fixtures do not meet them even when the correct wattage was used - mainly due to lack of ventilation around the lamp.
If you then use higher wattage than rating, you make itway worse.

Exceeding these means life and reliability problems. This is valid for all things, by far not only lamps.

There is 3 more in the basement the exact same, and never have issues with them, and their bulbs last for 3 or 4 years. Those ones have plastic or brass sockets, I can't remember.

It's just cheap bulbs.  The bulbs are the $2.99-for-12 Home Luminaire bulbs. Sometimes the sockets are a bit loose out of the box to begin with, but I use them anyways and they work until they break.

But then why the bulbs fail in that way only in some places?

There's no water leakage, but we have had cool nights and hot days lately.

It does not have to bethe real water leakage, you say there arelarge differences between day and night temperatures, so I would even suspect water condensation from the air. It could be enough to wetten the cement and then when combined with the excessive temperatures, it fails earlier.

By the way the better quality bulbs do not have as much better cement, but the glass is shaped so, the bulb remains fixed (just by the shape) even when the cement looses it's strength (after e.g. the long term heat/humidity exposure).

Another update. The new bulb I just put in died. The glass had a fracture (but the bulb is still intact) around near the base. All the gas escaped from the bulb, and filled the globe of the fixture. I put a new bulb in the fixture again, and just put the wire bulb guard back on WITHOUT the glass globe. This is only temporary, I will be buying a new fixture.