It seems that many of us (myself included) have learned the importance of backing up one's hard drive the hard way: when the hard drive crashes and the data saved on it is lost forever. There is no excuse in this day and age of affordable backup options for such tragedies to continue.
There are several simple and easy solutions, ranging from a tiny USB drive that fits in a pocket for smaller quantities of data to external, portable hard drives that can copy the entire hard drive of a laptop or desktop computer.
Additionally, cloud computing solutions (i.e. Apple's MobileMe and Microsoft's Cloud Power) are becoming more abundant each day, and there are many websites that can be used to store and share particular types of files. For example, even though I backup all of my photos to an external HDD, I also upload everything to Flickr with a Flickr Pro account - $24.95 a year for unlimited storage space, and it doesn't diminish the resolution nor the quality of the images. Another, more comprehensive online solution would be Crash Plan, which also for $25 per year (and a free 30-day trial) allows hard drive data to be backed up online and to additional computers.
In case your backup plan some how fails (or you never bothered to back your files up), there are a few last-ditch efforts to recover at least some of your data. One solution is DriveSavers, which employees a team of technicians who will "perform microsurgery" on a hard drive in an ISO 5 cleanroom to recover what information they can.
In case you're undecided or having trouble deciding on an external hard drive and/or back-up source, check out some of ZDNet's recent coverage of portable storage media below to narrow down what is right for you and your computing needs: