|I'm assuming that you HAVE NOT dropped the external hard drive. If you HAVE NOT dropped it, or otherwise damaged it's connection at the drive, there's probably nothing wrong with the circuit board inside the external drive|
Your problem is VERY COMMON.
The USB port you plug the external drive into MUST be able to actually supply 500 ma of current.
The external drive may NOT be detected correctly when it's plugged into a port in an external USB hub, or a port on the front of a desktop case.
It's very COMMON for people to DAMAGE the data on an external drive because they DID NOT do this....
If you have unplugged the external drive while Windows was running WITHOUT clicking on the Safely Remove Hardware icon and choosing to STOP accessing the drive BEFORE you unplugged it, you can damage data on the drive, and in that case, there may be NO drive letter for the drive that shows up in Computer or Windows Explorer, and in Disk Management the space on the drive will show up as being RAW or un-allocated, or unrecognized. . That can usually be recovered from if you use certain programs to repair the data damage, WITHOUT you losing all or most of the data that you know was on it previously.
However, DO NOT RUN CHKDSK on the drive !
(Type: diskmgmt.msc in the Start Search box, press Enter, to go to Disk Management. If the drive doesn't show up there, the drive is not being detected at all, for whatever reason. )
Troubleshooting USB device problems including for flash drives, external drives, external memory card readers.
See Response 1:
In addtion to that info....
For some desktop mboards you can have problems when an external hard drive is plugged into one of a pair of USB ports on the back of the case that are connected to the same USB controller, if there is another device plugged into the other USB port for the pair, because the pair can't actually supply 500 ma per port - they can only supply 500 ma in total. Usually those pairs of ports are one above the other, not beside each other. If you have two devices plugged into such a pair of ports, try plugging one of them in elsewhere on the back of the computer.
For MANY laptop and netbook mboards similar applies. The built in USB ports often cannot actually supply 500ma per port - they supply 500 ma in total for two ports that are close to each other. In that case, the external drive should work fine if it's the ony thing plugged into the USB ports built into the laptop or netbook, or if you have more than two ports, the only thing plugged into two ports close to each other.