I'm posting this because I find it will be useful for a lot of people, you can link here if you need (an article about this would be useful too). You can use this method to backup your files from Windows XP, Windows Vista and Windows 7, and I assume it will work for Windows 8 too.
First, you need to have a Windows 7 Install DVD. If you don't have one, you can get an official ISO image from this link:
You need to burn this to a DVD, or to create a bootable USB drive (with at least 4 GB). To do so you can use the Windows 7 USB/DVD Download Tool provided by Microsoft:
Instructions to use this tool can be found here:
Once you have a bootable DVD or USB, insert it in your PC and reboot. You will see a "Press any key to boot from CD or DVD" message. If you don't you will need to select the DVD or USB as your boot device. To do so you will need to press a key at the screen with the logo of the manufacturer of your PC. This depends on the manufacturer: for HP this is typically ESC or F9, for Dell you must press F12, and so on.
Once you boot from your DVD or USB, you will see a "Windows is loading files" message, followed by the Windows 7 "Starting Windows" boot screen. Next you will be presented with this screen. Select your keyboard layout and click "Next":
Then select "Repair your computer":
Let the system search for Windows installations. Then click "Next":
If no Windows installations were found (or if you use Windows XP), you will be presented with this "Select a system image backup" error message. Just click "Cancel" on both windows:
Anyways, you will get to this "System Recovery Options" screen. From here you could attempt to use System Restore or Startup Repair to see if you can fix your PC. To backup your files, select "Command Prompt":
Type "notepad" and press Enter. Notepad will open:
Go to File - Open. On the "Files of type" box select "All files":
Now you can go to "Computer" (at the left) to see your partitions:
Locate the files you want to backup, right-click on them and select "Copy". Typically your files will be at C:\Documents and Settings\UserName in a Windows XP environment, and at C:\Users\UserName in a Windows Vista or Windows 7 installation:
Insert an external HDD or USB drive, go to "Computer" again, and paste them there. Note you won't see any progress dialog:
Be careful not to double click a file, or it will open in Notepad. If Notepad freezes, you can go back to the Command Prompt, type "taskmgr" and use the Task Manager to end Notepad, then start again:
When you are done, close everything and restart your computer:
Please note, if you have a LOT of files to backup, this Windows Preinstallation Environment (Windows PE) will restart itself every 24 hours (but this should not be a problem to anyone, I say this just in case).