Sometimes the problem isn't with the hardware but with a key system component. In that case, you may be able to boot with a Linux LiveCD, mount the drive, and copy off all your crucial files. This trick works whether your hard drive was running Linux or Windows, as long as the LiveCD understands the filesystem on the drive.
Of course, that assumes you have space to which you can copy the data. Sometimes it's handy to just mount your laptop hard drive on a desktop PC to copy the data quickly. Unfortunately, laptops and desktops use different IDE connectors. But heeeey, that's not a killer problem. Cables to Go makes a laptop-to-IDE hard drive adapter that lets you hook up the notebook drive to your desktop PC. I just ordered one this morning -- the cheapest I could find was at TechSunny.com.
I gotta admit, I'm not cool like the Fonz, but I know NewsForge readers are. Got any more tips like this you'd care to share?