What do you mean by "sometimes the tire"?

Does it happen only when you're riding, never when inflating?

Are you sure it's the tire/tube, and not related to spokes or hub?

My wild-ass guess is you might have a spoke shifting around at the rim. You might put a drop of lube (and then wipe clean) on each spoke nipple.

Edit: Oh, I had assumed by "pop" you just meant a popping sound. But now I realize you're more likely talking about the tube actually popping and deflating? In which case I agree with the other poster about spoke holes and checking the rim tape.

Likely culprit it an exposed spoke hole. Check your rim tape and see if there are any voids between it and a hole, guaranteed flat. If so, buy some new rim tape and should be good to go. If not, do you have the old tubes? Check the puncture to see if they are in the same spot, that will give you an idea what is causing it.

I had a run a few years ago of a flat every week or two until I learned this

What does the hole in the tube look like and where is it?

What do you mean by "pops"?

Same questions as others:
- Have you taken the time to carefully inspect the surface of your wheel rim?
- Is the rim tape intact and undamaged?
- When was the last time maintenance was performed on the wheel (truing, etc)?

As others have said. Check the tire and check the rim. Is there any debris lodged in the tire (or damage to the tire itself allowing debris to poke through), or is the rim tape damage, and possibly a spoke pinching your tube... That's your first line of defense, if neither of these are an issue, it may be with your technique in replacing a tube. If you don't make sure that the tube is well seated, and not caught under the bead of the tire, it may pop during inflation, or sometimes you can get a few rides in before it effectively chaffes the tube between the bead and the rim and then ruptures... the other culprit may be tire pressure and temperature... How high are you inflatting your tires, and what temps are you riding in... Over inflating tires and then riding as it warms up can be a recipe for blow-outs...