I mainly backup my website to my computer, and upload it to Dropbox, Google Drive, and other free storage sites for backups.
Subscribing to shared web hosting to use as a back up server shouldn't be too expensive for small websites, and you can also use it to host a website on.
A bigger sized USB flash drive may work as well since a lot of small websites, blog and forums can fit in a single flash drive because the MySQL Databases are usually under 4GB in size, and most members host images and videos on Tinypic, Imageshack, YouTube, Vimeo and other external sites and social networks because it is more convenient, and faster than using a forum's web host server.
DVD-R, and Dual Layer DVD-R could also be enough space to store a few small websites.
Flash drives and Discs can be better since they don't have any moving parts, so they are less likely to break when dropped from a table.
Backing up locally is always good, but imagine how long it would take to download an extremely large site? That's where things like off site backup solutions come in handy.
Would it be possible just to use a script, FTP, SSH, etc and another shared or VPS web hosting account to backup websites, and databases?
I think bigger sites have multiple servers located in different locations around the web, so if one server goes down, another server can take over the traffic from the server which is down.
Really Big sites also have multiple domain names like Google has Google.com, Google.ca, Google.co.uk, etc.
I think Wikileaks used many servers around the globe, and registered a ton of domain names, so when one server, and domain name got banned, the content is still viewable on other domain names and servers around the world.