Problem

Some PC video cards come with a TV-out connector that is S-Video only. But you want to connect it to a VCR or television which only has composite video inputs.

Solution

Build a passive adapter. The S-Video signal is nothing more than a NTSC/PAL signal, where the color component kept on a separate line. The S-Video signal is combined onto a composite using this simple circuitry:
     __   __
    /  |_|  \          ____ 
   /         \        /    \(c2)
  |(s1)   (s2)|      ( (c1) ) 
  |(s3)   (s4)|       \____/
   \         /         RCA
    |__===__|         male
     S-Video
      Male
s1---------+----------------------c2
           |
s2---------+

s3-----------------+--------------c1
                   |
s4-----------||----+
             C1
I've built this adapter and can confirm it works.

Source: http://www.hut.fi/Misc/Electronics/circuits/svideo2cvideo.html
Thanks to lj and netsharc for pointing out a mistake. (c1,c2 reversed in circuit diagram)

A Better Solution

Because IANAEE, this 'naive engineer' solution is imperfect. It will degenerate the quality of the signal. If you plan on recording to VCR, it may not even matter. The properly calibrated circuit can be found in jasstrong's s-video node. I've never wound my own inductor, I think I'll try that version too.
Comments on roded's Cat5 octopus wiring:

To minimize the chance of crosstalk between audio and video (nasty 50/60Hz and 15kHz hum and hiss), keep the pairs together when wiring up the connector.

For example, use the OrangeWhite/WhiteOrange and GreenWhite/WhiteGreen pairs for S-Video, then the two remaining Brown and Blue pairs for audio (or just one of the pairs for SP/IDF Dolby Digital sound. Also, use the color-striped white wire of a pair for the ground signal.


On TenMinJoe's TV screen overscan adjustment:

For recent ATI video cards equipped with TV out connectors (from Rage 128 to Radeon), surf to ATI's support site(http://support.ati.com) and download the ATI Control Panel drivers. This driver installs new tabs in your Display Properties control panel.

One of them, labelled ATI Displays (accessed in Settings->Advanced) shows all the connected monitors. Click on the odd-shaped button above 'TV' to view its properties, then select the Adjustments tab which shows screen position and size controls.