How to test HDD for health?

To check your hard drive's health, try using S.M.A.R.T. drive diagnostics:

All modern drives have a monitoring technology called S.M.A.R.T. (Self Monitoring Analysis and Reporting Technology) that continuously monitors a number of parameters on a hard drive. Many parameters can be monitored by S.M.A.R.T. including read and write error rates, seek error rates, spin up time, temperature and much more.

(Summary taken from techsupportalert.com)

Many programs support S.M.A.R.T., but I personally use the PartedMagic LiveCD's built-in utility to do this. Because this is a Linux LiveCD, you might want to use a native Windows program. Good choices are:

• HDDScan

  Supports various S.M.A.R.T. settings and diagnostic tests as well as a "conveyance test" (travel damage) that might suit your needs.

• Crystal Disk Info

  Open source but supposedly does not have as many features as HDDScan. I've never used it so I can't jusdge the veracity of this.

• SpeedFan

  Though this is usually used for CPU and hard drive temperatures (and of course fan speeds), SpeedFan also has a little S.M.A.R.T. tab from which you can run diagnostics.

Check the manufacturer's site. - Seagate offers SeaTools, WD offers WDDIAG etc.

On the one hand, you could apply the "Error-checking tool" of Windows like this:
Randomly right click a partition in “My Computer” to select “Properties”=> Open “Tools” tab and hit “Check Now”.
On the other hand, you could check it at the aid of special software, such as Seatool.