It doesn't matter how old or how new your computer is, you need to back up the files that you don't want to lose. If you are like most people, you tell yourself, "Aw, that would never happen to me." True, you probably never will have any trouble losing computer data or files unless you really start putting things on your computer that you can't replace: stories you've written, photographs, your whole recipe file, your banking system. Tragic things like loss of computer data never happens to people unless you can't afford to lose the data---then, chances are you'll lose it. That's sort of like Murphy's Law (if things can go wrong they will).
When people used typewriters for their writing, they often added a sheet of carbon paper and secondary piece of paper in the typewriter to keep a copy of their work. Now, with computers maintaining everything a person does in life, people have actually become less cautious about losing that important data. People put so much faith into their computers, that they just can't imagine a catastrophe happening with no way to retrieve that data.
The last time one of my computers crashed with no way to restore the functionality, the computer was 731 days old---that's two years and one day old. To clarify that, it was exactly one day out of warranty. I'm not good at reminding myself to keep computer disks of my important data. Thankfully, I'd just purchased an online back-up system which takes a complete disk image of my computer--8 gigs worth of information. Because I had this external system, I lost no files.
However you chose to back-up your files depends on how conscientious you are at backing up your system, how easy you want it done with nothing to do on your part, if you want something that is relatively cost-free to back up or has a small fee involved. There is no one-best method for everyone.
If you are using a computer which still uses magnetic disks (floppies), it would not be advisable to keep using those for your storage. Magnetic tape can be damaged and lose data. Plus, if that computer crashed, it's not as easy to find computers now which can read those disks.
CD's or DVD's can still be wonderful ways to store data for long term use, but that can get costly, and cumbersome to store. Plus, those can get scratched making them unreadable. Flash drives (more commonly called thumb drives) are great for transferring data from one computer to another, but they are not advisable for long term storage. External hard drives are fairly reasonable in cost and are a great way to have a secondary way to store data, but you have to manually remind yourself to make copies onto your external hard drive. There are now automatic external back-up hard drives that simply plug into your computer and automatically start copying your data. However, some of those are not programmed to operate as well if you are running Windows Vista 64 bit.
On-line back-up systems are becoming more and more popular. The prices vary but are relatively inexpensive and can be purchased yearly or by the month. Some banks offer computer back-up systems as part of your package with banking at a particular bank.
Before making any decisions for on-line back-up systems, if you know someone using a particular system, find out how satisfied they have been. Find out if they are using the same type computer system you are when comparing. Read reviews in reputable computer magazines or on-line computer reviews affiliated with places such as PC Magazine or CNET. Also, find out how easy it is to restore your computer system if you have a computer crash or if you have to completely replace your computer.
Back-up systems can work remotely and seamlessly, but you are entrusting your information to travel through cyberspace (though it is encrypted) and to be stored out of your reach.
Don't let anyone convince you there is only one way to back-up your computer files. You need to decide for yourself what works best for you. And, . . .there's always the old fashioned paper back-up system, too.