It works quite well, in my case. There is only one pitfall: conflicts. Since two edits on the same line become a conflict, this can easily cause headaches unless some sort of agreements or conventions are in place. For somebody acquainted with git, it's not bad, but typically if somebody doesn't use git, svn, etc. and they have a conflict, the merge process is far from painless. The best way to avoid this is simply to add newlines as frequently as possible, after every sentence as a minimum; also, have some sort of understanding with your co-authors about who is working on which sections. This may or may not be easy for you, depending on the technical content of your writing.

For my own notes and papers, it's great in all the ways that git is supposed to be: keeps me organized, keeps things backed up (I use BitBucket, free unlimited collaborators with a .edu address), and makes me feel better because I have more control over the whole process (as opposed to Dropbox or Google Drive).

I wrote my thesis with latex + git. Merging can sometimes be wonky, but no wonkier than usual.

I had my sister review my thesis for grammar and spelling, she doesn't do git, so I checked out a coy in a dropbox folder and shared it with her. She made her edits in the folder, and would send me emails as she finished each chapter. After she finished a chapter I would check in her changes and merge the diffs with FileMerge.

Worked pretty well, though we only collaborated on text, I never merged figures or equations. I also had a cron job that would render the head of the master and put it on my website so my advisor and committee members could check in on my progress.