(1) Using an external USB or FireWire type drive, make an immediate backup copy of everything most-critical to you. rsync is very good for this. (Mind you, I'm not saying this because the disk test will put things in danger, but because you may not have done this in a long while...)
(2) Boot the computer from a LiveCD. You need to test a hard-disk while it is un-mounted.
(3) Disk-checking tools like e2fsck have a -c option which will cause the badblocks program to be run, and which will incorporate that information into the filesystem, i.e. by marking the bad sectors so they won't be used.
(4) Something very powerful that I only found about myself very recently .. thanks to this very forum .. is smartctl. It turns out that most IDE drives have on-board diagnostics which can be run. The smartd daemon can even run them periodically and e-mail you when there are problems. (You learn something new every day...)