Helping people with computers... one answer at a time.
Relying on free email services - even GMail - can be an unnecessary risk. Fortunately GMail makes it possible, even easy, to backup your email.
You've mentioned backing up GMail to somewhere on your own computer; how do you do that?
Of all the current free email services, GMail is my favorite. I know I've railed against free email services as your only email service, but they definitely have their place. And GMail is the service I recommend.
In part, I recommend it because I can answer this question. GMail is easy to backup.
In a nutshell, the way to backup GMail to your own machine is to use a "traditional" email client, like Outlook, Outlook Express, Thunderbird or others, and configure them to use GMail's POP3 access to download your mail.
Now, depending on how you use GMail there are a couple of approaches to doing this.
First let's set you up with POP3 access.
POP3 is the way traditional email programs that run on your PC get your email from your ISP. One of the reasons I recommend GMail is that they support using POP3 to download mail from your GMail account.
To start, you'll need an email program. Chances are you already have Outlook Express on your machine, and while that's better than nothing I actually recommend Thunderbird, also free, as good, reliable and feature rich email program. Perhaps most importantly for our backup purposes, your email in Thunderbird is stored as text files rather than Outlook Express's proprietary and somewhat error prone DBX files.
Once configured, when you go do download or "check for new mail" using your email program you'll get your GMail. The first time it could be a lot, depending on how long you've been using GMail and how much email you have.
Do that periodically, and the mail that's store on your machine is your backup should you ever lose anything from GMail. You might even consider backing up those files along with your regular PC backups.
And of course, you could consider simply using your email program instead of the GMail web interface, since you now have that as an option.
If at any time you want to re-download all the mail in your GMail account, you can. GMail help includes instructions to backup all mail by forcing GMail to download all email, even that which might have been downloaded before. That's a good way to create a snapshot at any point in time.