First I should point out that excess or increasing noise could be a sign of a failing hard drive - this is true in my case and I've ordered a Samsung SpinPoint HD501LJ(external link) as a replacement. Use a tool such as HDTune(external link) or SpeedFan(external link) to check your SMART attributes for signs of failure.

As a quick fix I cut some strips of anti-slip matting roughly 1"x9" to wrap around the drives and absorb some of the vibration that was making my HDD cage vibrate and hum.

I also added some matting above and below the cage to stop the general vibration of the cage passing to the rest of the case.

Results: Great reduction in noise, the PC is noticeably quieter with the side off. Very quick to do and minimal cost at less than £4 per roll, which could do about 50 drives.