S-Video write up by 2542787/#2558854 anon

[What is S-Video]

S-Video (AKA Y/C, Super Video, Separate Video) is an upgrade from composite signal.
It separates the luminance signal (Y/luma) and the chrominance signal (C/chroma).
It uses a 4 pin mini-din connector also known as ushiden.

[Benefits]

It's a huge quality upgrade over RF or composite ; going from S-video to RGB/component yields a much smaller quality jump.
In north america it's fairly easy to find a CRT TV with S-video input and for some devices like projectors it's the best connection for a console.
240p consoles benefit the most, DC and beyond should use RGB, component or VGA if possible.

[Cons]

Some games were made with composite in mind, this is especially true with many US Genesis games because its 320 horizontal resolution interferes with composite encoding. In these games you will see typical vertical dithering pattern with S-video instead of expected blending. Despite this, many times the clarity gain is worth it because the game is colorful enough (both Earthworm Jim are good exemples). Some others like Vectorman 1 get plain ugly though.

[Consoles with native support]

Super Nintendo/Super Famicom
Nintendo 64
JP/NA Gamecube
Wii
WiiU
Playstation
Playstation 2
Playstation 3
Xbox
Xbox 360
Saturn
Dreamcast

[Consoles with mods that enable S-video]
Master System
Megadrive / Genesis (most of them)
Neo-Geo
NES / Famicom

[Getting the best out of S-video]

While S-video is a great upgrade, you can still run into quality troubles.

It's best to add an S-video port to use a regular S-video cable even if your console natively supports it ; high quality ones are cheap.

If you want to use a S-video cable made for your console, you risk running in the dreaded checkered pattern.
Contrary to what info is mostly found on the internet, the pattern is not caused by composite signal being routed on Y/C pins, most cables are actually wired correctly ; it's caused by luma and chroma wires being too close to each other.
http://i.imgur.com/IaNPAcp.jpg
http://i.imgur.com/LuCk2UD.jpg

Some say that a cable with no yellow composite plug is less likely to have the pattern, but this is false as well. Look how thin and close those wires are.
http://i.imgur.com/Yl177f7.jpg
http://i.imgur.com/WKKqocA

Outside of using OEM cables which are generaly high quality, you can try opening the connector and replacing the S-video wire with a thicker, higher quality wire ; even if they're not shielded, the simple fact that each have thicker insulation and that each has a ground wire can be enough to stop interference. It's then up to you to make look as good as possible.
http://i.imgur.com/36uH2nF.jpg

If you want to try your luck and buy one, try to find a cable with thick wires, or at least with the S-video wire being thicker than the audio wires.

[Console specific]

PAL Gamecube doesn't support S-Video.

N64 stock can't output more than S-video.

PAL N64 requires additional components on the Y/C lines, can be put in either the cable plug or in the console itself.
http://i.imgur.com/UeL08aW.png

PAL Super Nintendo requires additional components but only on the C line. Note that exact capacitor value does not matter much, I used 100nF and it worked fine.
http://i.imgur.com/u7H4N6V.jpg
http://i.imgur.com/Pv9Fhrt.jpg

PAL Megadrive modded to 60hz won't output color because chroma subcarrier frequency is derived from master clock divided by 15 for NTSC or 12 for PAL. On a PAL Megadrive, 53.2034/15=3.546893 mhz which is too far from NTSC 3.579545 mhz. Solution is to either also replace the master clock with a 53.693175 oscillator (but you won't get color for 50hz).
Or build a small circuit that will always provide a correct frequency no matter what mode is chosen. This might also be true for Master System.
http://i.imgur.com/xQjW2R0.jpg

Megadrive/Genesis, depending on encoder used, the circuit is not the same and some cannot be S-Video modded.
NES/Famicom requires a NESRGB board which is a fairly extensive modification. Once done, wiring is straightforward.

French RGB Master System 1/2 have no video encoder and thus cannot be modded.

[Misc]
PAL color encoding is slightly better than NTSC, even with S-video ; reds tend to bleed less. If your display supports it, you might want to set the encoder in the console permanently to PAL. This is especially true with PAL Megadrive as switching to 60hz also changes encoding. Super Nintendos are already set permanently.
PAL encoding + 480i/60hz + 4.43mhz subcarrier = PAL60, not a standard but usually largely supported on euro TVs.
PAL encoding + 480i/60hz + 3.57mhz subcarrier = PAL-M, used in Brazil. Subcarrier isn't exactly NTSC but very close.
NTSC encoding + 480i/60hz + 4.43mhz subcarrier = NTSC443, also not a standard but usually supported.

[Links]
Checkered pattern (go for pics, not for explanation)
http://www.micro-64.com/features/svideo.shtml

S-video mod for consoles using Sony CXA1145
http://www.jamma-nation-x.com/jammax/genesismods.html

Gallery, some pics found, some taken myself
http://imgur.com/a/OQEnX