I have solved this problem in various ways, but my two favorites have been:

1. Flex Tubing otherwise known as Split Loom.

This stuff made the cords behind my A/V rack very neat and tidy looking. It had the following disadvantages, though:
- Lots of forethought needed to get all the cords organized well in the first place. The split loom was just the thing that wrapped up all the cords and made them invisible.
- Making modifications to the A/V equipment was, afterwards, more difficult because I needed to re-incorporate my changes into the split loom. It was a Big Deal to add or remove a piece of gear.

2. Custom backboard!

This one was a fun project. I moved into a brand-new house recently. The house includes a large mantlepiece painted gleaming white in the center of the living room. The top of the mantlepiece was VERY deep. It's about 6 feet wide by about three feet deep. Plenty of space for a big screen TV and a bunch of AV gear stacked up on either side of it. And if all the gear is at the front edge of the mantle, then there is about 1.5 feet of space behind it. Plenty of space for the rat's nest to run wild and free (and easy to maintain). But it was ugly. So here's what I did.

I bought some gleaming white already-pre-made shelving from the local home supply store. The longest one I could get was about the width of the mantlepiece. Also bought a smaller one to cut up for "ears" on the back of it. Screwed it together with some L-brackets on the inner-facing sides and it made a perfect "hide" for the cables. Notch a few "mouse holes" in strategic places on its bottom edge (cords from the AV gear tuck into the mouse holes), and bingo, no more cable mess. All hidden behind the gleaming white "hide" doohickey I made.

Hard to put into words, here's a thousand of them: