Question: Are there any free tools available to perform hard drive diagnostic?
I have an old 3.5 IDE Samsung HDD which I use as an external drive through USB connection. I recently started to have problems with accessing some of the data.

Answer: 
Along with all the other suggested options, you may want to look at more basic hardware factors:

* try using a different usb cable
* try a different usb port on the computer
* try using the hard drive in a different external drive case
* if available, try using esata
* try connecting the hard drive directly to your motherboard and see if the problem occurs

And as always, if you think the drive is flaky, make a backup of the data on it asap. It will protect your data from a drive that may be dying and give you the option of doing destructive data tests if need be.
You can grab Hiren's boot cd which contains some free tools for this purpose. [Website is here](http://www.hiren.info/pages/bootcd)

Maybe you'll have to attach your drive to the IDE bus for doing your maintenance work.