Yes (in most cases)
If your TV has multiple inputs (say S-Video, Composite, or Component, etc.) AND a coaxial cable TV connector, then the answer is yes provided that you have a coax cable splitter, and sufficient coax cable to supply the TV and VCR with independent RF signal.
Connect the splitter to a cable connected to the wall outlet, and one each from the splitter to the TV and the VCR. You VCR output will have to use the alternative connection to your TV (component, or s-video in most cases)
Many different vendors sell RF coax cable splitters (like Radio Shack, Best Buy, etc.) Make sure that you get a good quality splitter that has a large frequency range (e.g. 5-1000 Mhz), or you may have problems. Most splitters that are rated for use with cable modems should work.
Note, that with FiOS TV, only analog channels (in most cases under channel 50) are available without a cable box. If you have a cable box, then you will need to decide which device (VCR, or TV) will get the cable box connection, and which will live with just the small number of analog channels.
Written by Don - David Horn
Last updated on 12.22.06