Can you record a cable program on your VCR if your cable is run to the TV without a cable box?

Yes, you can as long as you have the coax cable connected to the VCR first and then to your TV.

Some TVs have RCA A/V outputs also and you can connect a VCR to them.

Even better is to use the RCA A/V connections from the cable box to VCR, VCR to TV.