As an ancient computer user (dinosaurs and abacuses), I have simple and reliable methods of backup. I would never trust a backup program made by Microsoft.
First of all, what do you back up? There are methods for each thing.
Every email that I want to keep is saved as a file into a folder, usually named 'saved_emails' - and I always use DOS conventions to name my folders and files, for example - keep them free of all punctuation, use few characters, use underscores rather than hyphens, and no spaces.
Bookmarks from both Firefox and IE are backed up into a file.
Finance software such as Quickbooks or Quicken or Microsoft Money are backed up into a file.
Keep things together. Pictures in pictures folders, etc, documents in documents folders. I never used "My Documents" much, preferring to make my own folders, partly because I always used to store all my documents on a separate partition to make it easy to re-install Windows.
Now, you have to decide what you want to use to back things up. Backups are often not as reliable as you may think. USB thumb drives are pretty good for transferring files, but not so great for long-term storage. External hard drives are great, but keep in mind that if a lightning strike takes out your computer and your external drive is hooked up it will probably be fried as well. Offline backup is OK if you trust the government to stay out of it. I don't.
CD disks and DVD disks are probably a good storage choice, will last for years in a cool, dry place. They can bugger up, so it helps to make more than one backup. Regular backups are the best and the disks are cheap.
So, next is to have a dependable disk writer. I use CDBurnerXP Pro, partly because it will also effectively burn ISOs, which bundled Nero programs won't do. If you don't know what an ISO is, don't worry about it until you need it. You may never need it.
Since you've taken the time to back up all the stuff I listed above to a file on your computer, the next step is to simply copy the stuff from your folders onto the disk.
Start the disk-writing program, put in a CD or DVD. Keep in mind that a DVD will hold a whole lot more than a CD, but then needs a DVD drive to copy the files to another computer.
Simply copy all your files onto a CD or DVD or break them up into blocks that will fit on the disks. Put them in a safe place.
One last note: if your computer did not come with re-install disks but does have a program built into the system to make your own disks, do it! Don't depend on a backup partition on the hard drive because there are only two kinds of hard drives - those that have failed and those that will.
Every time I use my business software, I back it up before I close it in several places - an external drive, a thumb drive, a flash card. I used to use floppies, but they're pretty obsolete these days. I never, ever, depend on a single backup of things that are important to me.
TEST your backups. Look at the disks. If you have important business software or accounting software, try it on another computer - install the program and see if it will take your backup. I had one computer customer who had a computer crash and had only made backups about every three months - and it was Peachtree software. Turns out, the data backup was useless without also backing up the program settings. On another computer, you can install the program, put in the program backup, then the data. But they were left with nothing.
My old version of Quickbooks needs a separate backup for each company, and I have two - so each time I use it, I backup each company to the business data folder as well as the external backups. I've re-installed it so many times over the years that I am sure it works.
Sometimes, it can be good to just start over without all the junk you've accumulated over the years, but with people using digital photos as their only pics of their growing kids or other relatives and weddings and so on, you really need to work at keeping your data safe.