Digitizing Commercial Videotapes
Most commercial VHS releases include Macrovision copy protection, which prevents copies from being made by including a series of high-voltage pulses in what's called the vertical blanking interval, a part of the image that's not visible on the screen. When a DVD recorder detects these pulses, it does not allow the content to be copied.
A device called a digital video stabilizer, such as the Dimax Grex (shown above), can be used to circumvent Macrovision copy protection. Simply connect the output of the VHS player to the input of the stabilizer and the output of the stabilizer to the input of the DVD recorder. Then, connect the audio output from the VHS player directly to the audio input of the DVD recorder. (In addition to composite video as shown above, the Grex includes S-video connections as well.) Of course, I don't advocate using such a device for commercial piracy, but I have no problem with using one for personal backups.
I've never used such a device, so I don't know if it reduces the picture quality, nor do I know if it significantly delays the video with respect to the audio, but I wouldn't be surprised if it does either or both. In any event, the source material is pretty low-quality to begin with, so if it were me, I'd replace the VHS tapes with Blu-ray if available or DVD if not. I'd only copy the VHS tapes that aren't available on any disc format.
If you have an A/V question, please send it to firstname.lastname@example.org.