A discrete RGB signal yields the best possible picture you can get in terms of analog video (component is about equivalent). Luckily most consoles will put out RGB without modification, but there are a few different forms of it. The Genesis, SNES, and Saturn can output RGB with composite sync (RGBS), while the Playstation 1/2/3 can only output or RGB with composite video as sync (I'll call this RGBC), or RGB with sync on green (RGsB). The Dreamcast is great because it can output RGBS, RGBC, or RGB with separate horizontal and vertical sync (RGBHV, also called VGA). I think the XBox 360 is the same way, I know it can at least do RGBS and RGBHV. The Wii is a little different in different territories. I haven't messed with it yet, but I will eventually.
I had to mod my NES, PC Engine, and N64 for RGBS (see next post). The Gamecube can output RGBHV, but I had to find a console with a digital video port and modify an expensive cable (more below).
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As you can see, the problem with hooking up and switching a lot of consoles is handling all the different types of signals. What I do is use custom cables for all my consoles. They are wired a to DB15HD (VGA) connector in the following pinout:
1 Red
2 Green
3 Blue
4 (unused, reserved for future use)
5 Ground
6 Red Difference (Pr)
7 [Luminance (Y)]/Composite Video
8 [Blue Difference (Pb)]/[Chrominance (Cr)]
9 +5 volts
10 Composite Video for Sync
11 Left Audio
12 Right Audio
13 Horizontal Sync
14 Vertical Sync
15 Composite Sync
By connecting only the appropriate pins for the desired signal type, these cables can carry composite video, S-video, component, RGBS, RGBC, or RGBHV, as well as analog audio all in the same cable.
Here's an example for one of my favorite consoles, the Super Nintendo:

I bought an RGB SCART cable for the SNES on eBay, removed the SCART connector at the end, and soldered the appropriate wires to a d-sub connector. In this case: red, green, blue, c sync, +5v, audio left, right, and ground. Then I secured the connector in a d-sub hood for protection and strain relief, and snapped it shut.

This is typical for several consoles, and can be wired easily, given these pinouts:
http://members.optusnet.com.au/eviltim/gamescart/gamescart.htm]http://members.optusnet.com.au/eviltim/gamescart/gamescart.htm]http://members.optusnet.com.au/eviltim/gamescart/gamescart.htm-
These cables are then connected to a custom switch box that is wired to my pinout:


This is a 4-way switch I made with color adjustment and sync processing. Four custom cables coming from the consoles are connected to the four inputs, A, B, C, and D, and one is selected with the switch on the front.
The audio from the selected console is outputted to the two RCA jacks at the top, which go to the equalizer and then to the receiver. If the cable is carrying composite video, S-video, or component, it is outputted to the three RCA jacks at the bottom (composite comes out on the green jack; S-video comes out on the green and black jacks and requires a small adapter; they didn't have blue RCA jacks in stock at Digikey, so I got a black). These other video connections are there in case the need arises, but I'm mostly concerned with RGB.
The switch box has a simple circuit inside that will convert composite sync or composite video to horizontal and vertical sync. This means that regardless of whether the selected input cable is carrying RGBS, RGBC, or RGBHV, it will be outputted as RGBHV in the standard VGA pinout to the d-sub connector in the center. This can then be connected with a standard VGA cable to my transcoder. The TC1600 can actually work with c sync on the h sync pin, but there are a couple of reasons for me to use separate sync at all times.
Before reaching the switch, the red, green, and blue color lines of each input all run through 100-ohm tweaker potentiometers. This allows the red, green, and blue color levels to be adjusted individually for each input. After the switch, the red, green, and blue lines run through 220uf capacitors.

This is what the switch looks like inside. It looks like an impossible rat's nest at first, but it's not really that bad once you start working on it. When you buy these, the d-sub's and the switch are already wired. All of the guts can be unbolted and removed as a single piece to drill all the extra holes for my added parts and put them in. Then I just needed to reroute a few of the lines going to the output, and the red, green, and blue lines coming from the inputs. About three quarters of the wiring didn't have to be adjusted.

That blue thing in the center is the heart of the switch. It's just a simple rotary switch that all the connections run through.

This is the sync circuit. It uses an EL4583 chip to seperate sync, and two CPC1002N optical relay chips to pass the horizontal and vertical sync created to the appropriate output lines. The circuit is activated and powered by +5v coming from the selected input (luckily all the consoles that output RGBS or RGBC output +5v). So when pin 9 is not powered, the optical relays disconnect the circuit from the output, and native RGBHV sources can pass their sync straight through to the output. This also means that the switchbox requires no external power supply.

EL4583 and CPC1002N's can be bought from Digikey.com. The datasheets are available here:
http://www.intersil.com/content/dam/Intersil/documents/el45/el4583.pdfhttp://www.clare.com/home/pdfs.nsf/www/CPC1002N.pdf/$file/CPC1002N.pdfThe only other thing going on inside electrically is the potentiometers on the input color lines and the capacitors on the output color lines.
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Here are some more examples of cables I use:

Here's one for the Playstation 1/2/3, and one for the Genesis. The Playstation cable I used had that A/V breakout halfway through. It's not really in the way of anything, and could be used to pass composite to a Guncon or something.

This one is for Dreamcast is a little different. It has some DIP switches on it to activate the mode select lines on the console's video out. These allow for selection between two 15kHz RGB modes, or 31kHz RGB (VGA). More info here:
http://www.gamesx.com/wiki/doku.php?id=av:dreamcastav
This one is for a Gamecube. In order to get RGBHV out of one, you have to hack an official component or d-terminal cable, and modify the connections to a chip found inside the cable. I could only find a component cable and it was pretty expensive. I removed the original output cable, and wired it up as a small adapter dongle with a female d-sub in my pinout. I also integrated the standard connector to add audio. A standard VGA cable can be used to connect between this and my switch box. More info here:
http://gamesx.com/wiki/doku.php?id=av:gamecube_rgb
Since I had the other halves of the cables I used for this sitting around, I figured I'd make something out of them. This can be connected to my Gamecube dongle for component video. You need to set the DIP switches on the dongle for RGBHV or component.
This cable can also be connected to my Playstation cable with a gender changer for component video. This works because of the shared pinout. You just need to switch back to component in the display settings.
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Anyway, this is what can be done with d-sub connectors and switch boxes and such. The connectors are a lot smaller and easier to work with than SCART connectors, and the switch boxes are also very cheap ($12-15 USD) and versatile. They're small (about 6x2x4 inches), non-directional, and don't require a power supply.
The main limitation of the switcher is of course the limited number of inputs, but you can chain them together. Three 4-ways chained will give you ten inputs. They don't add any more resistance in the lines than a short length of wire, and I can't see any reduction in brightness when compared to a straight connection. Of course, only the one at the end of the line needs a sync circuit, filter capacitors, audio breakout, etc.
It doesn't have to be as complicated as mine either. The color adjustment pots are not totally necessary, and depending on your sources and your monitor/transcoder/scaler/video processor/whatever, you may not need a sync circuit. You could easily use a d-sub switch without any modification this way, and you might be able to use a DB-9 instead of a DB-15. An audio breakout, SCART connection, etc., can be provided with a custom cable connected to the output.
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My multi-console arcade cabinet will have various systems connected this same way, but I'm working on a circuit that will do the switching with relay chips instead of a physical switch. This will allow for some fancy tricks.