Clonezilla to the rescue!
One of my computers (I have seven) started reporting that SMART (http://en.wikipedia.org/wiki/S.M.A.R.T.) had detected that the main hard disk was about to fail. Luckily the disk could still be read and I had just been reading about Clonezilla (http://clonezilla.org/).
So after a quick trip to the local computer store to buy a new 1TB drive to replace the existing 500GB one, I then downloaded Clonezilla and burnt a boot disk. As the computer already had two drives installed, I had to temporarily remove the good data drive so that I could clone the failing main OS drive.
Once the new drive was in place, the computer could be booted from the Clonezilla disk and the failing disk cloned onto the new one. This took just over an hour and once it was complete the failing disk could be removed and the new disk swapped into its place. After reinstalling the data disk, the computer booted as if nothing had changed, except that now the main drive had a lot more free space.
The hardest part of the process was driving to the store and physically swapping the drives around. Too easy.