Question: I use a version control system (formerly subversion, now git) to write papers, which for me works very well and is convenient. A few times, I even worked with branches for different logical versions of a paper, such as versions submitted to different journals. However, I found branching of little use for paper writing. When I used different branches for different journal submissions, I found myself working only on the "latest" branch anyway, since I can anyway only submit one version per time, and, if it is rejected, will not continue to work on that particular version at a later time. I didn't find any other good use of branching in paper writing, and later skipped it completely.

Is there any advantage of working with several branches when writing a paper with a version control system? How should one organize the writing process in order to profit from such an advantage?

Answer: 
I use HG, but it is essentially the same as GIT, in that branching is easy. I branch all the time when working with coauthors. The branches tend to be short lived and merged pretty quickly. Basically, I distribute a copy to my coauthors and each set of comments I get back form different branches. This lets me see each authors comments individually. I then work on merging the comments back into the main trunk. Sometimes the merge is easy and the branch is one commit long. Other times it might take longer if I need to work out something (e.g., math, model, or analysis) which might require a couple of revisions before it is ready to go into the main trunk.
Personally, I've never used branches (for papers), and would certainly *not* use branches for different chapters (WTF? like keeping different branches for different files in a programming project; except for the case when different collaborators edit different parts of documents, then - maybe), but maybe it may work for:

* arXiv/non-arXiv version (or e.g.: working version with notes vs release candidate) of a paper (the exact use-case of projects with some differences, from minor to e.g. also additional sections, see also [arXiv preprint and final paper differing by sections and appendices](https://academia.stackexchange.com/questions/1864/arxiv-preprint-and-final-paper-differing-by-sections-and-appendices)),
* [Beamer slideshows](http://en.wikipedia.org/wiki/Beamer_(LaTeX)) for different talks based an similar slides.

Related: [git + LaTeX workflow at SO](https://stackoverflow.com/a/6190412/907575) (so, use "advisor" branch):

> 
> Branches are also extremely helpful if you are a graduate student. As any grad student will attest, the advisor is bound to have numerous corrections, most of which you don't agree with. Yet, you might be expected to atleast change them for the time being, even if they are reverted later after discussions. So in such cases, you could create a new branch advisor and make changes to their liking, at the same time maintaining your own development branch. You can then merge the two and cherry pick what you need.
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;)