Throughout this answer I'll assume, that a storage drive appears as a block device at the path /dev/sdc. To find the path of a storage drive in our current setup, use:

• 
  Gnome Disks (formerly Gnome Disk Utility, a. k. a. palimpsest), if a GUI is available, or


• on the terminal look at the output of lsblk and ls -l /dev/disk/by-id and try to find the right device by size, partitioning, manufacturer and model name.

Basic check

• only detects entirely unresponsive media


• almost instantaneous (unless medium is spun down or broken)


• safe


• works on read-only media (e. g. CD, DVD, BluRay)

Sometimes a storage medium simply refuses to work at all. It still appears as a block device to the kernel and in the disk manager, but its first sector holding the partition table is not readable. This can be verified easily with:

sudo dd if=/dev/sdc of=/dev/null count=1

If this command results in a message about an “Input/output error”, our drive is broken or otherwise fails to interact with the Linux kernel as expected. In the a former case, with a bit of luck, a data recovery specialist with an appropriately equipped lab can salvage its content. In the latter case, a different operating system is worth a try. (I've come across USB drives that work on Windows without special drivers, but not on Linux or OS X.)

S.M.A.R.T. self-test

• adjustable thoroughness


• instantaneous to slow or slower (depends on thoroughness of the test)


• safe


• warns about likely failure in the near future

Devices that support it, can be queried about their health through S.M.A.R.T. or instructed to perform integrity self-tests of different thoroughness. This is generally the best option, but usually only available on (non-ancient) hard disk and solid state drives. Most removable flash media don't support it.

Further resources and instructions:

• Answer about S.M.A.R.T. on this question


• How can I check the SMART status of a drive on Ubuntu 14.04 through 16.10?

Read-only check

• only detects some flash media errors


• quite reliable for hard disks


• slow


• safe


• works on read-only media (e. g. CD, DVD, BluRay)

To test the read integrity of the whole device without writing to it, we can use badblocks(8) like this:

sudo badblocks -b 4096 -c 4096 -s /dev/sdc

This operation can take a lot of time, especially if the storage drive actually is damaged. If the error count rises above zero, we'll know that there's a bad block. We can safely abort the operation at any moment (even forcefully like during a power failure), if we're not interested in the exact amount (and maybe location) of bad blocks. It's possible to abort automatically on error with the option -e 1.

Note for advanced usage: if we want to reuse the output for e2fsck, we need to set the block size (-b) to that of the contained file system. We can also tweak the amount of data (-c, in blocks) tested at once to improve throughput; 16 MiB should be alright for most devices.

Non-destructive read-write check

• very thorough


• slowest


• quite safe (barring a power failure or intermittent kernel panic)

Sometimes – especially with flash media – an error only occurs when trying to write. (This will not reliably discover (flash) media, that advertise a larger size, than they actually have; use Fight Flash Fraud instead.)

• NEVER use this on a drive with mounted file systems! badblocks refuses to operate on those anyway, unless you force it.




• Don't interrupt this operation forcefully! Ctrl+C (SIGINT/SIGTERM) and waiting for graceful premature termination is ok, but killall -9 badblocks (SIGKILL) isn't. Upon forceful termination badblocks cannot restore the original content of the currently tested block range and will leave it overwritten with junk data and possibly corrupt the file system.

To use non-destructive read-write checks, add the -n option to the above badblocks command.

Destructive read-write check

• very thorough


• slower


• ERASES ALL DATA ON THE DRIVE

As above, but without restoring the previous drive content after performing the write test, therefore it's a little faster. Since data is erased anyway, forceful termination remains without (additional) negative consequence.

To use destructive read-write checks, add the -w option to the above badblocks command.

fsck - check and repair a Linux file system. Invoke it using

fsck /dev/sda1

where /dev/sda1 is the drive you want to check. See 'man fsck' for more details.

There's also 'badblocks' command which checks a device for, you guessed it, bad blocks.

The drive need to be unmounted when checked, so to check the root partition you need to create a file 'forcefsck' in the root of the partition and reboot. The device will be checked upon the next boot:

sudo touch /forcefsck

sudo reboot

Alternatively, you can boot from a Live CD and run the check from there.

badblocks

You can check for badblocks running the command

1. 
   sudo badblocks -nsv /dev/[device-partition] > bad-blocks-result for a non-destructive read-write test. That will generate a file called bad-blocks-result with the sectors damaged.
   
   
   
   

   • 
     

     -n Use non-destructive read-write mode. By default only a non-destructive read-only test is done.

     
     

   
   

   • 
     

     -s Show the progress of the scan by writing out rough percentage completion of the current badblocks pass over the disk.

     
     

   
   

   • 
     

     -v Verbose mode.

     
     

   
   
   
   


2. Then, you can run sudo fsck -t ext3 -l bad-blocks-result /dev/[device-partition] to tell the file system where the bad sectors are and move data away from them, if possible.

You can find more reading about it here.

smartctl

IMO smartctl is a better tool. You likely have to install it first

sudo apt-get install smartmontools 

Then

sudo smartctl -a /dev/sda | less

to print drive health data, attributes, and available test results. To quit less, type q. Alternatively

sudo smartctl -H /dev/sda

to just print health data.

To begin a new short (a few minutes) or long (up to many hours) self test in background:

sudo smartctl -t [short|long]

GSsmartControl
(home page) and Gnome Disks are graphical front ends if you prefer.

See also

• Smartmontools


• http://www.cyberciti.biz/tips/linux-find-out-if-harddisk-failing.html


• http://www.techrepublic.com/blog/linux-and-open-source/using-smartctl-to-get-smart-status-information-on-your-hard-drives/

F3 (Fight Flash Fraud) is another option which should additionally detect fake flash drives (flash drives whose actual capacity is a fraction of advertised capacity):

1. 
   

   Install F3

   
   
   

   sudo apt install f3
   
   

   
   



2. Insert your drive



3. 
   

   Write test data to the free space on the drive (check where your drive is mounted with lsblk)

   
   
   

   f3write /media/$USER/D871-DD7C/
   
   

   
   


4. 
   

   Read the test data

   
   
   

   f3read /media/$USER/D871-DD7C/
   
   

   
   

Reference:

• f3 documentation site


• Source code

Badblocks works well but it isn't designed for detecting fake flash drives and may not report any errors for them.

You can test-read the entire disk, while showing a progress indicator:

time sudo pv /dev/sdc >/dev/null

Certain disk problems would manifest as reported I/O errors. This is a bit nicer than dd due to the progress indicator and because the command-line interface is a bit more standard and a bit less typo-prone. Note that pv is basically and enhanced version of cat. It may not be installed by default, but can be installed with sudo apt-get install pv.

A similar approach is to read the disk with one of the several available tools that are specifically aware of disk I/O errors -- and have the feature of "trying hard to rescue data". Search for ddrescue in the package manager.

If you have a partition that you CAN NOT LOOSE THE DATA follow these steps

1. Determine which partition you want to check for bad sector using the

$fdisk -l commnd

Lets assume that the partition to check is called /dev/sdPTC (partition to check)
and that you have another partition to store the results mounted on /scan/resultPath/ folder

2.Then you can run this command

$sudo badblocks -v /dev/sdPTC > /scan/resultPath/badsectors.txt

which will determine what are the bad blocks of the given device and store them on a file called badsectors.txt

3. Now you can use fsck command to tell Ubuntu not to use the bad sectors mentioned in the badsectors.txt file.

$sudo fsck -l /scan_result/badsectors.txt /dev/sda

That way life of the hard disk is increased a bit until you get a new one for replacement.

If you have a complete partition that you want to check for bad physical sectors and you CAN AFFORD LOOSE ALL DATA on that partition or is EMPTY follow these steps

1. $sudo apt-get install gnome-disk-utility




2. $sudo gnome-disks




3. Check and double check that there is no important data on that partition




4. Using gnome-disks DELETE/REMOVE the partition by hand using the "-" sign




5. Using gnome-disks CREATE a new partition and select the "slow" option that will check the given space for errors