Hello,
I have some helpful info for you guys...
There is an electrical term called 'impedance' you should become familair with. It is a circuit's (a cable is a circuit) resistance to an AC waveform (audio and video are AC waveforms).
Audio is such low frequency that impedance doesn't really matter that much, and depending on the equipment, it can be 1K to 47K ohms. Audio cables are cheap cables that are not impedance controlled, they will vary, and the consequences are little.
With video, impedance does make a difference, and most video equipment and cables are 75 ohms. However cheap OEM video cables that are not 75 ohms will cause a problem, mostly with high bandwidth video such as HDTV. Xbox, PS2, and GC, are all capable of producing high bandwidth HDTV signals.
Congratulations, you have just graduated from VU, Video University.
Now, the $30 mechanical switch boxes barely perform with composite video going through them, and if you try and send through HDTV, you will see a softening of the picture, and possibly image ghosts or double lines. Might be OK with you for 480P (non HD games), but ugly on 1080i games. Of course, all this is assuming you are viewing on an HD ready big screen, which if you are not, get with the program!

Here are some links and comments to component video switchers I have found on other forums, from highest to lowest cost:
http://www.keydigital.com/detail.asp?Product_ID=KD-SW4x1Switches video, coax digital audio, analog audio, from an IR command. Nice, but $599
http://www.zektor.com/home_theater.htmSwitches video, coax digital audio, optical digital audio, analog audio, from and IR command. Price is $299, so it doesn't exactly meet the price target of $100
http://www.audioauthority.com/aacconsumers/1154c.htmlPrice on this one is $194, so still not low enough, but cheaper. Switches video and audio as well, but uses signal sensing to try and figure out what to watch. Works for some people, but others have found problems with it.
http://www.inday.com/rgb4x/rgb4x.htmSwitches only video, but low cost at $149. Enclosure is not to elegant, but gets the job done.
http://www.avtoolbox.com/avt-5842.htmSwitches video, and analog audio, but no digital audio. Price is $89, so it meets the $100 target. However, word of caution, there are many reports of this one have poor video quality or other problems. Now the Inday people have posted a technical review which reviels why:
http://www.inday.com/reviews/rgb4x-review.htmSeems you get what you pay for. I'm not sure that this would even be suitable for 480P non HD games.
There is also a JVC mechanical switch that appears to be designed for component video, but when I researched all these options a while back, I was mainly focusing on things that can be remote controled.
So in my somewhat-professional opinion, I prefer the Zektor switch, and it is working nicely for me.
http://www.zektor.com/hds4/index.htmThat is all, back to work.
-The Unit