I believe in Mathematics and Computer Science journals usually accept LaTeX documents. In fact, the AMS has a number of packages and document classes for just this purpose.
What about other disciplines? I'm not particularly familiar with the humanities. Would a Microsoft Word document be unacceptable?
Does it vary from subject to subject, or even journal to journal?
The policies vary entirely from journal to journal about what is considered acceptable. APS journals, for instance, will accept both MS Word-based documents as well as documents formatted with RevTeX, their modified template system. ACS journals and a number of other publishers also offer their own LaTeX- and Word-specific templates for authors to use. Whether the use of the template is required or merely recommended is also a function of the journal. So, as a general rule, you should always check the homepage of a journal before you start preparing an article for submission to that journal.
To some extent, I prefer working with LaTeX in preparing manuscripts, for the simple reason that their plain-text document format makes it a lot less painful to switch back and forth between different templates, compared to a word-processing format like Word or LibreOffice or Pages.