Western Digital (500GB WD Caviar, WD5000AAJS 32YFA0) from a MyBook chassis. Original symptoms were no sound/no spin-up and blinking light circle on the external chassis.
I extracted the drive and attached another power supply (I no longer trust the original power supply), then smoke started coming from the controller board. Disconnected power immediately.
I removed the controller board/circuit board and located the smoking component by reattaching the power for a few seconds: it turned out to be the TVS-diode [Transient Voltage Suppression], marked "TB13A V721").
I then found a page explaining the function of TVS-diodes at
http://forums.seagate.com/t5/Barracuda- ... m-p/118908.
After reading this thread, I removed the diode by desoldering each side.
When I reapplied power to the board, no smoke or other visible things happened.
I then remounted the controller board and applied power -- DISK SPUN UP AGAIN!!!

Hooked the drive into an USB-port on my computer, using a SATA to USB controller -- Windows installes drivers....
At first, disk management found the disk, but was unable to initialize it, but when i plugged it into another USB-port the darn thing worked like a charm!
However, now the drive is no longer protected by the TVS-diode, so I'll just hurry up and copy the contents when I get my replacement drive in the mail.
Thanks a lot, people of this thread, for giving me the courage to try this. I feel awesome now!