This might be of interest;
Have a external Western Digital MyBook 1TB that just stopped working one day - stone dead symtom. It has Firewire400 (which I used), USB and eSata ports. Hopeful that the disk inside would still be intact, I went and purchased a HDD docking station with USB 3.0. I went for the USB 3.0 version, because I was also upgrading my computer from the first Macbook Pro (Intel) to the mid-2012 Macbook Air.
When the stuff arrived, I tried out the docking station on my old Macbook Pro - this worked excellently, and I was much happy to have my data back.
Moving to my new mid-2012 Macbook Air, the drive didn't work at all. I could hear it spin up, but nothing more happened. It did not appear in the disk utility list, nor in the system info. Tried all solutions mentioned; reset PRAM, et cetera.
I had an idea, and plugged it into my USB2.0 hub where I have my keyboard and mouse connected to my Air, and guess what - the drive works...
So we can pretty much sum it up to some USB 3.0 related issue.
More detailed info:
The docking station seem to be some generic chinese stuff, unfortunately, but the box text says; Computex Taipei (no other logo; this might just be some award they won), and "Hard Drive Dock Pro" is the name of the device. It's a 2,5" or 3,5" SATA HDD dock. Bought it from a Swedish retailer, and here is the product page;
http://www.dustin.se/product/5010400605/usb-3-0-dockning-till-2-5-och-3-5-sata-h arddiskar/
The exact name of the HDD is Western Digital WD10EACS - 00ZJ80 (or --B0) from 30 nov 2007, and it's a 1TB Green Power drive.