The popularity of LaTeX varies by field. In math and physics it rules, and will continue to do so. In other subjects it doesn't.

However where you want to use TeX or LaTeX is for any documentation which you want to archive. Word is simply a horrible choice for this. While it is a good bet that people today can read Word, it is a bad bet that in 15 years someone who finds a Word document will know what to do with it. However if you take a TeX document that was written 15 years ago, it isn't that hard for a person to read it in a text editor. Furthermore on the operating system of your choice it is possible to take the document and print it with the only difference from the original being caused by the limitations of your output format. (The output of TeX is specified down to the visible wavelength of light.) In fact the odds are extremely high that the program you would use 15 years from now is exactly the same as the one that you would use today. No matter what operating system you are on. (TeX is the only widely used program that I know of whose development has stopped. What people develop are macro packages to use on top of the basic program. But it has not been touched since March of 1995.)

There is no other document format which can make equivalent claims. For instance PostScript cannot readily be read as text, and the output is not even guaranteed to remain the same from one printer to another. Microsoft has problems correctly importing documents written 5 years ago. There are many minor variations on groff out there, and the toolset is not widely used outside of Unix.

It is to be hoped that tools like LyX will make more people get into TeX. But no matter what happens, there are niches which it dominates today that it shows no signs of losing its spot in for a very long time to come.