If your monitor doesn't have VGA (then it will have only HDMI or DVI) and your VCR supports either HDMI or DVI (very unlikely) then you can connect it and it will work. You can get adapters between these two formats the same as the analog formats.
Heres the problem: If your monitor only supports DVI or HDMI and your VCR only supports an analog format you're going to run into problems. You'll need to get a analog to digital converter to use it. These are hard to find and are increadibly expensive when you do. You'd be looking at $50-150 USD for one and even if you bought one theres a chance it might not work with your particular VCR.