I'm going to assume this is different from the normal soft click/chatter sound of a hard drive accessing data. To check, does it only make a click when the computer has been sitting idle for a little while? That would just be the drive waking up from a nap due to inactivity, and is normal. If it's more frequent, though, it could well be a symptom of a failing drive.
Smart Reporter is one way to ask the drive if it thinks it's ok, but it's easier to do this: Open your Applications folder, then open the Utilities folder in there; there should be a program called "Disk Utility". Open that, and click on the least-indented hard drive in its left pane (it will probably have a manufacturer name and a model number). Look down at the bottom of the window; it should say "S.M.A.R.T. Status: Verified".
If it says something other than Verified, then you almost certainly have a failing drive, and you should make sure that your data is backed up (of course, you should have anything important backed up ANYWAY, but now would be a good time to make sure), then if it's under warranty call Apple and get them to replace it.
If it does say Verified, that doesn't guarantee it's fine (you should STILL back up everything important), so you might still want to call Apple if it's under warranty and see what they say.
On a related note, unplugging the device without ejecting it properly will NOT break anything, and shouldn't have anything to do with the clicking. The worst that can happen is the data on the drive gets corrupted, which is bad for the data, but the physical drive is fine.