New node created on one site automatically created on others? Say I have a parent site where all my content is created: nodes and taxonomy terms, but I want that same content to be created - or to appear at least - automatically on multiple child sites. What ways could this functionality be achieved? The solution could be a custom module or a a contrib module, if one exists to perform this task.
Isovera wrote a good article on how to do this "Syndicate content between Drupal"

You'll need Views and Feeds at a minimum to get started.

In views you'd create an RSS feed (there are several views modules available to help with this) for the data you'd like to share between sites. You would then set up Feeds to import your newly created RSS feed. You can map each field from your feed to the content type you'd like to import into. Feeds can be configured to run on cron, allowing content to be imported from one site to another.