Christina Warren’s tutorial is geared towards users hosting their sites at MediaTemple, but since the important piece is the Ruby script that sends the data to S3, you can use the same technique at just about any web host. It will compress not only your web documents but your MySQL databases.
The only thing you’ll have to watch out for are things like file and directory paths. What’s great about this method is that you setup a script that will run, via cron, as often as you want, so you could easily have monthly, weekly, daily and even hourly backups if you wanted to run it that way – all safe, secure and if you want, encrypted.
This tutorial goes into a bit more depth, and shows that you can also use a similar setup even on your Linux or Mac desktop. At that point, though, you’d be better off using a front-end that does all the heavy lifting, like Jungle Disk.