There are many reasons to backup your personal files. Formatting your hard disk and starting again with a new operating system is a very strong reason. No matter how hard you try to remember everything, there are bound to be files that you'll forget. This list will hopefully get you thinking, so that you don't forget quite so many.
Photos and creative works
Digital photos are surely at the top of the list of files that you don't want to lose, but also think about other creative works that you've crafted yourself. Be it homemade videos, graphic art, audio creations, or even a game level you spent hours putting together, you'll be annoyed if you suddenly realise that you've wiped the disk without rescuing these files.
If you have a file that contains the passwords for your favourite websites, make sure you create a backup. And, if the file is encrypted, as it should be, make sure you consider how you'll restore such a file. You may need special software to decrypt the file, and possibly keyfiles, in which case you'll need to backup those too.
Some people delete their email as soon as they've read it. Other people save email that goes back for several years. If you like to keep hold of your email archives, make sure you know how to make backups of your email files, and how to restore them when necessary.
A long list of bookmarks that point to the finest sites on the web is something that you'll be sorry to lose, so make sure you create a backup of your web browser bookmarks.
Downloaded files and purchased software
Backup any treasured files you've downloaded, especially files that you've paid to purchase from online software vendors. Also remember to create a backup of any software registration keys that you'll need to activate purchased software.
Love to relive the best bits of Half-Life 2 or Doom 3, using your hard-won save files? Then remember to create backups of these files. Same goes for screenshots and videos you took of your avatars in action.
Music / media files
Ripping CDs into digital audio files is not enough fun to want to do it twice for each CD. So it's probably worth finding enough space to create a backup of your entire audio collection. Well, at least the parts of the collection you still listen to. Don't forget about movie files.
If you're required to file a tax return, you'll probably have spreadsheets or invoices stored on your computer that you are legally required to keep safe. If your hard disk fails and you haven't got a backup of such items, you could be in trouble.
Students and employees who work from home may think that "my computer died" is a great excuse to get an extension on a deadline, but it's no fun when it does actually happen. Backup your hard work.
Appointments, to-do list, address book. Check that you know where to find the files that store these details, and create a backup.
Sure, your web pages are already sort of backed up by being available online. But think about any behind-the-scenes files that you won't have put online, such as XML files, XSLT files, images in proprietary formats, new sections that haven't gone live yet, and old pages that you've archived.
If you use a decent operating system, you'll know the value of carefully crafted configuration files. If you've spent hours poring over man pages and online tutorials to produce the perfect configuration for your DNS or web server, it's a shame to forget those files when creating a backup.
Backup all of your source code files, documentation files, and project files. Unless you're a software company working for the British public sector, in which case just accept that you've done an awful job, and start again from scratch.
Once you've got a fresh install of an operating system, you'll be glad for the time saved by keeping a copy of all of your network connection settings and passwords. Think about the local network configuration as well as the settings provided by your internet service provider.
There are bound to be other files that I've not thought of. Last time I created a backup before overwriting the disk, I forgot to backup the Palm Desktop organiser file. So that file was lost forever. If you're diligent, or just paranoid, make sure to scour the directories on your hard disk, more carefully than I did.
Keeping a physical backup on an external drive and leaving it next to your computer is better than nothing, but won't be much use if your property suffers a fire which destroys both the master and the backup together. If you care about your backup then take a look at my review of a data safe which is resistant to fire and to the minor flooding caused by fire hoses.