Why?

Your Windows registry holds all the most important information about your computer. The registry knows what kind of hardware you have, what software is installed, and how you have Windows setup. Backing it up when your computer is running well can be very useful if you run into problems further down the road.  If you can't figure out why your computer is crashing, you can try restoring your registry later. 

How?

1. The registry really exists as two files:

c:\windows\system.dat
c:\windows\user.dat

I also like to include these two files in my backups as they control how windows starts and hold additional information:

c:\windows\win.ini
c:\windows\system.ini

The first two files are actually "hidden" and "restricted," so by default you cannot see them. In a Windows Explorer window, go to View-Folder Options-View and look for an option that says "Show all Files" and select it.  You will then be allowed to see these hidden files.  Go to My Computer-C:-Windows to see the files and scroll down until you find them.. 

2. The simplest way (but not the best way - see below) to backup these files is to *copy* (make sure you don't actually move them) by right clicking on the files and choosing copy.  Then go to My Computer-C: and make a new folder by right clicking and going to New-Folder.  Name it backup. Double click on the backup folder and right click and choose paste. 

3. That's it, your registry is backed up!

4. *Now for the safer way to do this.*  Boot your computer with a boot disk or by pressing F8 just before your computer says "Starting Windows..."  Choose Command Prompt Only as your boot option. Now type in these commands in sequence to backup your registry:

cd c:\   (takes you to the root of c:)
mkdir backup     (makes a backup directory)
cd c:\windows     (changes directory to Windows)
attrib user.dat -h -r   (makes file not hidden/restricted)
attrib system.dat -h -r     (same)
copy user.dat c:\backup     (copy file to backup folder)
copy system.dat c:\backup     (same)
copy win.ini c:\backup     (same)
copy system.ini c:\backup     (same)
attrib user.dat +h +r     (gives attributes back to file)
attrib system.dat +h +r     (same)

Now you have properly backed up your windows registry. There are other ways of doing this, but I have found this to be the most effective.
*TIP: You can copy and paste the commands above into a file in Notepad with slight modifications (no "cd" commands. Instead just use full paths for each command i.e. copy c:\windows\user.dat c:\backup). Then save the file somewhere as backup.bat.  Then  you can just run backup.bat anytime to backup your registry (preferably after booting to DOS).

You might want to look at HowTo Restory my Registry.