My setup used to look a lot like SLOweather's. It was pretty awful (no offense intended.)
The good news is it was easy to take care of, once I put my mind to it. I first used a Brother labelmaker to print up tags for each power brick so I'd be sure what it was used for (after the first 12 they all start to look alike.) Then I gutted the area under the desk, disconnected every cord and brick and emptied it out. I bought a couple of large multi-outlet power strips (12 outlets each, with nice separation for putting bricks side-by-side.) I then mounted them high up under the keyboard tray. The bricks were plugged back in, and to minimize the mess the cords were each wrapped short, near the brick.
I bought the 50-pack of velcro cord ties, and highly recommend them.
Yeah, it's still kind of a mess, but it's not gotten much worse in the year since I rearranged everything.