When it comes to collaborative editing, Google Docs is the go-to for most. But if you're looking for something easy that doesn't require a login, Fiddle is a simple Markdown editor for collaborative editing.
Fiddle runs in your browser and can save Markdown files both online or in your Dropbox. You can then share a link with someone and Fiddle creates a new document for them to edit. Every time you share a link, a new version of the file is created. It doesn't have the same type of live editing as something like Google Docs or Office 365, but the file versioning is an approach that might be useful for other types of projects.