One or more of the hints below will probably sort out most USB problems with most USB portable / external hard drives and OTHER devices (though not always)

A few things to check but assumes USB and Windows for other interfaces / operating systems (mac/ Linux) similar steps may be adapted to suit.

1. Ensure it is connected directly to the computer to a USB 2.0 port not a USB 1.0 port as this can have effects on performance and reliability

2. Use only the cables that came with it NOT one that fits that may have been lying around or is longer. Not all USB cables are equal even though they should be)

3. Do not connect through an external USB HUB unless that hub is USB 2.0 AND has its own power supply.

4. Use ONLY the power supply that came with it if it has an external power supply Don’t use any other unless you know it has both the same voltage and current rating e.g. 12V 500mA anything rated below that would not work properly.

5. Always use the same port for connecting your devices. Some devices do not like being switched about. If switched they may want to install software / drivers again. This can be especially true if you move a HUB to another port

6. For FLASH DRIVES you should ensure that the device is set for "quick removal" using the drive control panel properties or use the USB "Safely Remove Hardware" option. If you dont do this there is a very strong chance that any files you transfer may not be there when you plug into another computer.
7. It is possible to remove drives from the enclosures in most cases and connect directly inside a PC to fully check it.
You should also do this to cheack the drives connections are not bad inside the enclosure.
　
8. If none of the above steps help look at updating the drivers from the manufacturers web site in the support section.

9. If you checked and fixed anything there and still have issues then check your hardware from CONTROL PANEL / SYSTEM / HARDWARE.
Any exclamation marks by hardware need fixing before you investigate any further
10. ensure that you have set removable drives for "quick removal" or that you use the "Safly Remove Hardware" option often shown on the lower toolbar.It is possible that files my not be fully written to external devices before they are removed. This corrupts the file itself and even on occasion the drive.
SPECIAL NOTES
USB flash drives can fail for no apparent reason.
Sandisk Cruzers are especially bad for this.

USB hard drives should be treated with extreme care.
This is a real hard drive ! and knocks and bumps can quite literally kill them.

Note that if you hear a drive clicking or pinging this could be the worst thing you would hear.
Known as "The Click Of Death"
Hope this gives you the information you need

Bob
Moderator

It would be very decent of you to consider the quality of our experts answers and judge them accordingly as you pass through FixYa.

Thank you

Great answer already but a couple of additional things to try.

1. When you power on the drive place your hand on top of the enclosure and feel for movement. No movement could be a sign of failed HDD, power brick, or enclosure.

2. Most power Bricks have lights that indicate if they are receiving power or not.Check to make sure it is lit up. You may also want to listen closely to the power brick to try and identify humming. Loud humming in these devices are often symptoms of failure as well. If any of these occur you may want to consider ordering a genuine replacement form the manufacturer.

3. If you are tech savy and have access to another enclosure try removing the drive and transplanting it into a known good one.

4. keep in mind that all drives will fail eventually. Its best to back up critical data on multiple forms of media. There are some companies that even rent back-up space online. Off-site storage is always a good idea.

5. If your drive has failed checked the manufacturer's warranty. You may lose data but still be able to get the drive replaced.

hope this helps.