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.
It does indeed vary from subject to subject, and journal to journal. I once got in a short argument with some math students who had asserted "If its going to be published, it needs to be in LaTeX", a disagreement that only ended when I went and found some submission guidelines. For three fairly good journals in my field (Epidemiology), you have some considerable differences.
American Journal of Epidemiology wants everything in either Word or PDF format - LaTeX documents are compatible with this, but its certainly not doing anyone any favors in terms of already being formatted. Epidemiology will accept LaTeX documents, but warns that the odds of typesetting and other erros increases in formats besides Word. Journal of Clinical Epidemiology only requires that an editable version be available.
So the de-facto standard in my field is Word, though of course there are ways around that. And then, as mentioned, there are formatting issues beyond just "what's the file extension?" How references, the text, and figures are reported - must odds ratios be graphed on a log scale or not?. How p-values are treated. What format graphics are allowed to be in, etc. As Fabian said, submitting to a new journal often involves combing through the same content to subtly tweak formatting.
This varies a lot between journals, and probably even more between different disciplines. In the life sciences Latex is rather rare, MS Word seems to me to be the most common format in my subjective observation.
But the actual document format, be it Latex or Word, is only part of the difference between journals. The exact rules on how to format a paper vary so much that you'll have to put significant effort into adapting the same manuscript for different journals anyway. Check out the Author submission guidelines for Nature or those from JACS as an example. They often regulate details like how the axis labelling in graphs has to look like. The journals also often have different length requirements, so you might have to shorten your manuscript if you decide to switch to a different journal.
