Well, it's a bit complicated to set up initially, but my neighbour did this using an old (now defunct) Hauppauge TV card (PCI) that I lent him, plus a video player.
Basically the analogue Hauppauge TV tuners usually also have a video/audio input. The Hauppauge TV software allows you to select that input and, most importantly record it! Even better the recorded files are usually standard MPEG format.
Once set up he had a nice "production line" running. He'd ready the video player paused at the start, start the software recording and hit play.
Then he'd go away and come back later. Didn't matter too much if he was late, plenty of free software for simple editing of MPEG's.
Over a few weeks he transferred his entire VHS library to MPEG format. After that you can do what you like to burn it to CD/DVD as required in your preferred format. Most modern DVD players will play MPEG's directly anyway, but creating "proper" DVD's is easy enough - it's built-in to more recent versions of Windows.