I just use Mail.app. My Gmail account is not only backed up but also indexed in Spotlight and always available for off-line access. You just need to remember to start up your mail client every once and a while.
I setup a script on my Ubuntu box to backup my gmail account daily with mbsync. See http://www.chrisstreeter.com/archive/2009/04/305/gmail-imap-... It uses IMAP and stores the downloaded mail in mbox format that you can view with mutt or pine. Every so often I archive the entire backup and backup that archive so I have a snapshot of the mail.
I didn't know that. I presumed wrongly that Mail.app wouldn't allow me to re-export my stored mail. Now I have the dilemma of choosing to go back to Mail.app (which I really liked) and lose my Thunderbird customization, or stick to Thunderbird :-)
Not really. If google somehow loses your mail, it's not like you'd switch to using mail.app. You'd use it to upload your mail back to google or another provider.
Mail.app quite easily saves messages (or groups of messages) as standard mbox files. Select the messages you wish to export, go to "File -> Save As..." and select "Raw Message Source" as your desired format.
If you're just looking to move messages to another server though, it's almost certainly easier to add a different mail server and drag/drop your messages to the new server.
Even easier if you want the whole thing, just right click on a mailbox and select "Archive mailbox...". It will save a copy in the mbox format in the location you choose.
I mirrored my Google Apps email account by setting up a rule to forward to my Microsoft-hosted Outlook.com account. It uses the same spam filtering system as Hotmail. A serious problem happened when perhaps 10 spam messages over a few days made it through gmails spam filter into my inbox, and on to my Outlook.com account.
Sadly when my gmail inbox started filling up with bounce messages from the MSN Postmaster, I realised that Outlook.com blocked my gmail account for spam abuse - SYSTEM WIDE. I was completely unable to send ANY mail to ANY Hotmail or similar Microsoft-hosted email service.
Dealing with the MSN Postmaster team was very frustrating. They told me to go to complain to gmail instead.
TL;DR: Don't forward all your email to Hotmail because their spam filter is so crazy, they'll eventually block your email address from mailing into Hotmail hosted servers again.
I just use Mail.app. My Gmail account is not only backed up but also indexed in Spotlight and always available for off-line access. You just need to remember to start up your mail client every once and a while.