Hi Chris,
It depends on the setup.
My server instances are quite small so I do weekly images of the whole hard drive, which are stored in the cloud. If anything goes wrong, I'd be able to restore that image, with a couple of clicks more-or-less.
If your database is on localhost, then you'd probably be better off writing a cron-job through the console.
However rackspace does offer what they call "MySQL cloud databases", which are hosted remotely (i.e. not on your cloudserver) and can be administered through the Rackspace control panel.
Keep in mind I am using the Rackspace service in the UK cloud, so there may be some differences compared to the US, although probably favoring the latter service, if any.
You do have to be quite experienced in setting up Linux Servers though, and have some background knowledge on TCP/IP, Port forwarding, and web servers like Apache, lighttpd, or nginx, plus whatever else your LMS requires (e.g. an application server like Tomcat).
However, once you get everything secure and running, I don't think you can beat the service, even from a value standpoint.
Hope this helps,
Alex