EssayTagger supports DOCX and DOC (most common), as well as RTF and TXT formats.
Basically, if they can save their work as Word document, all is good! Note: If you're using Google Docs, kids can export their work as a Word document: File > Download as > Microsoft Word (docx)
And if you enable Google Drive integration for your course, students will be able to pull documents directly out of their Drive accounts and submit them to EssayTagger without having to download or upload anything at all. Learn more: http://blog.essaytagger.com/2013/02/how-to-enable-google-integration-in.html