I just purchased a VGA cable over the weekend and have noticed the same issue.
I am using a Sony G540P 21" CRT for a display. In its day, this was a $1200+ PC monitor.
I assure you there are no issues with this display, as I use it for my PC's regularly.
When connecting an XBOX 360, the image looks washed out as others have said. Almost as if someone has raised the gamma correction to its maximum setting on the source device. This is especially noticeable when playing Condemned, which inserts bars on the top and bottom of the image to provide a 16:9 widescreen experience. The bars, which SHOULD be as deep a black as one can find, are a medium gray in color.
When switching to input 2, which I use for my PC's, I am rewarded with normal rich colors, and no washed-out look. Areas that are black look black, etc.
When I run the 360 through my Sony KV34XBR910 high definition TV using the supplied component video cable I am rewarded with the same normal rich colors I expect from every other source used on that TV.
In summary, This problem only appears to exist when using the VGA cable.