The Phillips AMBX is a ready made solution to this. They have full on commercial packages (big $$$), but also have a home PC version that supports a wall washer (the "ambient" lighting behind a screen) as well as lamp modules, fans (so you get that "wind in your face" feeling when palying driving games, I suppose

) and a keyboard rumble pad..
You can check it out here
www.ambx.comI've played with one, and intend on using it my cab eventually.
The main issue with any system like this is "detecting" the majority color on screen at any particular time and echoing that out to whatever LED driver you choose to use.
Of course, if you're looking to just drive LED's in some way (with fades, wipes, color changes, etc) you can do that really easily with arduinos, or a an LEDWiz a pc, and LEDBlinky, or a host of other ways, but that won't imitate the colors on screen.
I actually started a project once to do this.
My take was to grab 10x10 pixel captures of the screen at various points, average those blocks, then average the averages to get a general idea of the color to the left and right sides of the screen, then drive some LED's through an LEDWiz to follow along. Grabbing entire screens worth of pixels would take way too much processing time to do in realtime, unless you could sit in the pipeline (which is actually what the philips driver does). But that kind of thing is a bit beyond me (or the time I could devote to it).