I use LaTeX in an academic setting (theoretical linguistics) which only occasionally requires a lot of math, but I'm still saving tons of man-hours by using the LaTeX + Emacs + AUCTeX combo. Here are some frequent use cases where LaTeX blows a text processor out of the water.
* Bibliography. The median article length in our field is 30+ pages, with reference lists of 60+ not uncommon. Maintaining these in Word/OO is a nightmare, even with (non-free) bibliography software. RefTeX allows me to find and insert citations in a matter of three keystrokes, and whenever I reshuffle the reference list I'm 100% sure it's in order (i.e. everything I cite in the text is in the references and there are no uncited references)
* We don't use math, but we do use a lot of tree-like diagrams. Drawing these by hand is a chore; using logical markup to get trees which need zero to very little tuning saves enormous amounts of time and frustration.
* Floats and numbered examples. TeX floats are notoriously unreliable, but seriously, are Word's any better? And it gets worse with numbered examples (and pictures in numbered examples). For instance, a frequent feature of linguistics papers is an interlinear gloss: two or three lines of elements that have to line up with each other. These involve tables or tab stops in a word processor, and are notoriously fragile (e. g. if your sentence doesn't fit on one line, you get horrible issues with breaking lines).
All this is in addition to the common advantages like keeping track of numbering. These are all things that can be done with a word processor, but usually require significant amounts of time and self-discipline.
A lot of people in our department use LaTeX; most are not of the "programming" type, and are not deeply "into" LaTeX, interacting with the very basics and using some googling and copy-pasting. They still get much more satisfactory results in a shorter amount of time than the Word people.
* Bibliography. The median article length in our field is 30+ pages, with reference lists of 60+ not uncommon. Maintaining these in Word/OO is a nightmare, even with (non-free) bibliography software. RefTeX allows me to find and insert citations in a matter of three keystrokes, and whenever I reshuffle the reference list I'm 100% sure it's in order (i.e. everything I cite in the text is in the references and there are no uncited references)
* We don't use math, but we do use a lot of tree-like diagrams. Drawing these by hand is a chore; using logical markup to get trees which need zero to very little tuning saves enormous amounts of time and frustration.
* Floats and numbered examples. TeX floats are notoriously unreliable, but seriously, are Word's any better? And it gets worse with numbered examples (and pictures in numbered examples). For instance, a frequent feature of linguistics papers is an interlinear gloss: two or three lines of elements that have to line up with each other. These involve tables or tab stops in a word processor, and are notoriously fragile (e. g. if your sentence doesn't fit on one line, you get horrible issues with breaking lines).
All this is in addition to the common advantages like keeping track of numbering. These are all things that can be done with a word processor, but usually require significant amounts of time and self-discipline.
A lot of people in our department use LaTeX; most are not of the "programming" type, and are not deeply "into" LaTeX, interacting with the very basics and using some googling and copy-pasting. They still get much more satisfactory results in a shorter amount of time than the Word people.