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You can keep a backup of Appropedia by downloading all text content from Appropedia:Current dump. This is in xml format, which can be uploaded to another MediaWiki installation (via the admin-only "Special:Import" page on the target wiki). This dump is updated weekly.
You can also download just the pages you want (latest versions, with or without full edit history) from Special:Export.
We currently don't have an easy way to backup all images (although we do have our own backups). If you'd like to help with that, please leave a note at the Village Pump - thanks!