This is intended to be a one-stop shopping spot for testing your hard drive outside of Windows.  If you're able to get into Windows, some of the manufacturer's offer tests that will work inside of Windows.  FWIW - here's a free generic test that runs in Windows (select HDTune, not HDTune Pro):  http://www.hdtune.com/download.html 

Suggestions are welcomed!

What you'll need:
- a blank CD
- a computer with an internet connection where you can download a file, install a small program, and burn a CD (doesn't have to be the computer that you'll be testing).

1.  Determine the make and model of your hard drive

- In Windows XP - Go to Start...Run...and type in "devmgmt.msc" (without the quotes) and press Enter.  Click on the + sign next to Disk Drives and use Google to search the information listed there)

- In Windows VISTA - Go to Start...and type in "devmgmt.msc" (without the quotes) and press Enter.  Click on the + sign next to Disk Drives and use Google to search the information listed there

- From outside of Windows: Unplug the system from the wall, remove the battery (if it's a laptop) and crack the case open.  Look inside to locate the hard drive and write down the make and model number (although the model number isn't required for the test, it will help you to identify what sort of drive to replace if the test says that the drive is bad).

NOTE:  It's strongly recommended that you use the test from the manufacturer of your hard drive.  Most manufacturers build in tests that are only for their drives (in addition to the standard S.M.A.R.T. tests) - so using their test will give more accurate results.

2.  Locate the support website of the hard drive manufacturer from the following list and download the appropriate file to your computer.  FWIW - the first link for each drive usually contains more information/instructions about running the test.

Hitachi - http://www.hitachigst.com/hdd/support/download.htm#DFT  Download this image for CD's: http://www.hitachigst.com/hdd/support/downloads/dft32_v415_b01.iso

Western Digital (I've had issues with running this from a CD/DVD) - http://support.wdc.com/product/download.asp?level1=6&lang=en  Download the Diag504fCD.iso file on this page:  http://support.wdc.com/product/download.asp?groupid=601&sid=30&lang=en

Seagate - http://www.seagate.com/www/en-us/support/downloads/seatools  Download the Seatools for DOS ISO CD-ROM Image from this link:  http://www.seagate.com/www/en-us/support/downloads/seatools/seatooldreg (English version here: http://www.seagate.com/staticfiles/support/seatools/SeaToolsDOS213bEURO.ISO )

Maxtor - Seagate SeaTools has replaced the Maxtor diagnostics.  Use the Seagate SeaTools links above.

Toshiba - I'm unable to locate any tools for Toshiba.  I'd suggest the Hitachi DFT (Drive Fitness Test) from above.

Fujitsu - http://www.fujitsu.com/us/services/computing/storage/hdd/support/utilities.html  Download the DOS Diagnostic Tool Ver. 7.0 (For IDE/ATA/SATA Hard Drives from this link: http://www.fujitsu.com/downloads/COMP/fcpa/hdd/utilities/fjdt_700.zip  You'll have to copy the file to a DOS boot CD and manually execute the FJDT.exe file once you've booted to DOS.  If this is too difficult, use the Hitachi DFT (Drive Fitness Test) from above.

Samsung - http://www.samsung.com/global/business/hdd/support/utilities/Support_HUTIL.html  Download the Hutil 210 ISO (for CD-ROM drive).zip from here:http://www.samsung.com/global/business/hdd/support/downloads/Hutil210_iso_for_CDROM_drive.zip  You must unzip the file before you can burn (NOT copy) the ISO image to a CD. 

IBM - IBM has merged with Hitachi.  Use the Hitachi DFT (Drive Fitness Test) listed above.

3.  If you do not have a disk burning program that's capable of burning ISO images to your CD drive, I suggest this free tool:  http://isorecorder.alexfeinman.com/isorecorder.htm  Select the appropriate version by following the instructions, Install the program, then reboot your system.
FYI - an ISO burner will place files in a certain order on the disk, this is what makes the disk bootable.  YouCANNOT  just copy the file to a CD - it won't work!

4.  Insert the blank CD into the CD drive and dismiss any dialogs that may pop up.  Then right click on the ISO file that you downloaded and select "Copy Image to CD" (it should be the top choice on the context (right click) menu.  Follow the prompts to record the image.  Remember that the slower the speed you select, the less likely it is that there will be errors in the burn process.  Most disk images are small, so the process shouldn't take very long even at the slowest speed.

5.  Boot from the CD to run the test.  Here's a partial list of ways to access the built in boot menus of different systems.  Press the appropriate key when the first screen shows up after you turn the computer on.
HP/Compaq - Esc
Dell - F12
Gateway/eMachines - F10
Acer - F12 (not always)
Toshiba - F12 (older systems will be different)
Sony - usually will boot to CD, may ask you to "Press any key to boot from CD"
When in doubt, either access the BIOS (Setup) and make the CD drive the first boot device (before the hard drive), or post in the forums for assistance.

6.  Follow the prompts on the screen to run the test.  In particular run the Long/Extended/Complete/Comprehensive/etc test - as the shorter tests are not completely reliable.  My greatest experience is with the Hitachi DFT - and you can just press Enter (2 times) until you get to the screen where it asks you to agree to the conditions (press A), confirm the devices listed (press Y), select Advanced (press A), then Start (press S) there.
NOTE:  If you have more than one drive installed, run the test on each drive.

If you encounter any problems running the test - just post them to the forums and someone will be glad to help you out.