Anticipating the digital TV signals to be sent out soon, I was wondering what effect this would have on my VCR when recording TV shows, and playing them back. Will my current VCR work? Will I have to buy a new kind? I’ve read differing articles - some say nothing will change, some say the opposite, no clear answer. We do get cable TV. (Yes, I realize the VCR is going the way of the dodo bird, but we are simple folk, set in our ways, and tragically technologically impaired and have no smart young people around to set us straight.) What say you?
If your VCR is hooked up to cable, there won’t be any difference. If you’ve connected an antenna to your VCR, you’ll have to run the antenna to a digital converter, and run that into your VCR
They’re already being sent out. Now’s the time to figure out how to get your VCR working before you can’t get your stories recorded. 
There are situations where there will be a difference.
My VCR is cable-ready, that is, on old analog cable it does not require a set-top box. However, many cable companies are ditching their legacy analog service to go to digital. If you get digital cable, you will at a minimum need a set-top box from your cable company to use the VCR. You will have to set the VCR to either channel 3 or 4 to receive the signal from the cable box. If you get HD over cable the VCR will not be able to receive/record the HD channels.
This also means that if you are used to programming your cable-ready VCR to record shows automatically, you will no longer be able to program the channel in the VCR. You will have to set the cable box in advance to the channel you wish to record.
It will be at this point when the best thing for the OP to say is, “I will pay the extra $5 a month to get a DVR.”
However, there are plenty of cable companies that aren’t planning on going 100% digital any time soon, so the odds of the OP having to worry about this right now are slim.