While our Mozilla Mail tutorial focuses on Windows, keep in mind that Mozilla Mail is a "cross-platform" email client: it runs and operates the same way on Windows, Apple's Mac OS X and Linux.
The Mozilla Foundation also offers the standalone Thunderbird email client: see the Mozilla Thunderbird Tutorial
Backup and Restore Your Profile in Mozilla Mail or SeaMonkey Mail
Although it is unlikely to happen, a hard drive crash is always possible. In such event, even data recovery specialists may have a hard time saving your emails and contacts.
Fortunately, it is easy to backup your emails and address book in Mozilla Mail. In fact, we suggest that you backup the complete parent folder, not just emails.
Tip: compress your email folders to reduce the size of your backup data. To compress your folders, go to File > Compact Folders.
Backup Your Mozilla Mail Profile Using MozBackup
MozBackup is a free utility (program) developed by Pavel Cvrcek, a Czech student, designed to backup your Mozilla Mail profile, (as well as other Mozilla applications'.) Unfortunately, MozBackup is currently only available for Windows. If you are using a Mac or Linux, please see below how to backup your Mozilla Mail profile manually.
Once you downloaded and installed MozBackup, run it.
The welcome screen will open; click Next. MozBackup will switch to the Operation Type screen: from there, choose Backup a profile, and select Mozilla Mail from the applications listed; click Next.
The next screen, "Profile selection", lets you choose which profile to backup: you will probably see just one profile, "default". Select it, and click the Browse button; pick the folder where you want to place your backup file. (You can also take this opportunity to name the backup file as you like.) Click Save, and Next.
MozBackup will then offer you the option to password-protect your backup file, why not choose yes - just in case.
The next screen lets you pick which files to backup. We recommend that you pick at least emails and address books, and certificates (if any).
Click Next, and MozBackup will store backup information in the file your determined earlier.
The duration of the backup process will mainly depend on the amount of emails you have.
If you backed up your profile on your computer, it might be a good idea to store a copy of the file on an FTP server. (It is probably not feasible to email yourself the file to a free webmail account, as these backup files can get very large.)
Thanks, Pavel! The backup process is made smooth and easy. Pavel Cvrcek does not request donations, but encourages us to support the Bone Marrow Transplant Foundation 
Backup Your Mozilla Mail Profile Manually
This section will show you where your Mozilla Mail profile information is stored, if you want to backup your profile manually, or need to obtain information on what to backup to integrate it in a third-party backup solution. This information also applies to Mac and Linux, for which the MozBackup application is not (currently) available.
To determine where your profile is stored, go to Tools > Account Settings, the Account Settings dialog will open. Select the Local Folders entry on the left.
In the Message Storage fieldset, there should be a path under Local Directory. Copy the path, and navigate to it. (In Windows, after having copied it, click the Start button, choose Run, paste the path, and click OK.) This is the folder in which your email data is stored.
To back up the folder in which all your profile information is stored, go up three levels, so that you end up in the Profiles folder, of which Mail is a sub-directory. The Profiles directory contains a folder called [blank].default, (where [blank] is an unpredictable string of alpha-numerical characters.)
Restore Your Mozilla Mail Profile
Restoring your Mozilla Mail profile is the reverse of the backup process: simply copy the folder you backed up into your profile folder.

If you have used MozBackup to backup your Mozilla Mail profile, run MozBackup and choose "Restore a profile" from the Operation Type screen. If you password-protected your profile, you will need to supply it.


Email Clients Tutorials
Mozilla Mail Tutorial