You would need a TV card or DVR card on your computer to record it.  For example, an All in Wonder 9800 Pro would do the trick!  I have one for $250 if you want one.

Another alternative, I think, is to purchase a set top dvd recorder.  I have a cable dvr and I use the S-video out and audio out rca outlets on the dvr box to the S video in and rca audio inputs on the dvd recorder.  I can then make dvds of movies I have stored on the dvr.  You can buy a decent dvd recorder for $225-$300.  It also serves as a dvd player.

DVD is  a much better way to store movies than video tape which has a much lower resolution and degrades over a relatively short time.