EaseUs and Recuva are excellent software recovery programs, though how successful you'll be depends on the nature of the damage to the hard drive. If your PC can't read the hard drive, sometimes you'll have better luck with mounting it into an enclosure and connecting via USB (which allows you to try a few PCs). After that, specialized data recovery firms are your best option, though be forewarned they can go over $1000.
Generally speaking, the only good way to save data is to never risk it in the first place - a consistent backup plan for your important files is an important and basic part of PC ownership, like changing the oil in your car or the air filter in your furnace.