Use an Email Client Like Outlook or Thunderbird to Download Your Gmail
You can use Outlook or Thunderbird or another desktop email client to download your Gmail as POP3, which will actually store the messages locally in your email client. You can keep the messages in the email software or, better yet, copy the important ones to a folder on your hard drive. You'll need to enable POP3 access in your Google account settings, under "Forwarding and POP/IMAP"; you'll also find configuration instructions there for setting up POP for Gmail in your email client.
Note: you can also set up Gmail in your email program as IMAP. This, however, basically syncs your email from the cloud to your computer, so in case all your emails disappear from Google's servers (or another webmail provider), your email client might actually sync to the empty server and delete the local copies. If you do access Gmail via IMAP, you can drag or save the messages locally to your hard drive as a backup. Of course, you'd need to do this regularly--before any problems on the web server happen.
Use an Online Backup Service like Backupify
Backupify backs up personal information from Facebook, Flickr, Blogger, Google Calendar and Contacts, LinkedIn, Twitter, Picasa Web Albums, and more web services. The free account gives you up to 2GB of storage--note that your cloud data is backed up online, in the cloud (to Amazon's S3 storage, specifically), here.Use a Desktop Program like Gmail Backup
Gmail Backup (dowload for Windows from CNet | developer's site) is free software for Windows, Linux, and Mac that backs up your emails in your Gmail account, as well as the labels. You need to enable IMAP access in your Gmail settings (under "Forwarding and POP/IMAP"). You can specify a date range for the backups, and emails are stored as .eml files, which are accessible to email programs.
Use a script to Backup Gmail
You can use a script to automatically download your Gmail messages, creating a local copy of your email on your hard drive at whatever interval you like. The About Python Programming site has a 3-step tutorial for retrieving POP3 email with poplib that can help those technically inclined. Another example is Lifehacker's Back up Gmail with fetchmail instructions, which involve using the command line and running the Unix program fetchmail in a Unix emulator for Windows, Cygwin.
While using or writing a script isn't as straightforward as the options above, it requires fewer computer resources than email programs do to run.
