Hey everyone, as I've fixed this issue on my last 3 cases I thought I'd post my thoughts and the reason this is a common issue.
I just fixed this on my Thermaltake Level 10 GT case. (Previously on my Antec 300 and 600 cases). My issue, while similar, is interference from the video card while the video card is under load.
See attached image while I explain.
http://i.imgur.com/QWY44hq.jpg
The reason this happens is because the case design assumes that it is OK to connect the headphone jack to COMMON GROUND. You'll notice that the PCB is grounded to the chassis when it is attached (A) and that shares the ground with both the USB (B) and Audio (C). As people mentioned, you may see feedback from USB devices as the ground is shared. The truth is, this audio jack should not share any ground, and should only be grounded via the header back to the motherboard.
When Audio uses a common ground like this, it will pick up all sorts of noise that other devices are bleeding into the chassis. Isolating the ground to the audio header on the motherboard will resolve the issue, as the sound card SHOULD have proper noise filtering that won't allow garbage to back flow into the audio header.
With this case, cutting the PCB (D) as shown will both remove the shared ground from the USB (B) and remove the connection to the chassis ground (A).
If you are having this problem on a different case, just isolate the points as I have and make sure that your audio ground does not have continuity with the USB (B) or chassis (A) ground. Also NOTE that you must disconnect the audio/usb header from your motherboard when testing continuity, as the ground points will be connected through the motherboard and show continuity, which is normal. Disconnect when testing!
Let's hope some day case designers give their head a shake. Until then, good luck everyone.