In almost every application I've ever seen that uses math equations, it always supports LaTeX.
If LaTeX does so much more than just math equations, why is it the defacto standard for math equations? Isn't that akin to everyone deciding to use Microsoft Word's Math Editor for math equations?
Related question: Is there a name for the subset of LaTeX that deals specifically with math equations?
I think it's a survival of the fittest thing. First of all, math notation isn't specific to LaTeX, it's inherent in the TeX engine.
So what do we have:
I don't know what troff did for formulas (which might have been a competitor at the time), and I don't know whether Knuth invented it all by himself (was'nt there a system named scribe he used as a blueprint?), but I can imagine there was not that much pressure to ever develop an alternative aspiring for all these features at once.
You can look at MathML for the result what happens when such a thing is attempted by a committee ;-)
As the first two answers have already stated (La)TeX has become the defacto standard in several areas because it is basically good at what it does, fairly natural to author and freely and widely available.
It's also I think instructive to see where (La)TeX did (or has) not become ubiquitous. @stephan-lehmke mentioned MathML. The downside of TeX being so flexible (which is what makes it excellent as an authoring format) is that it is hard to process with anything other than TeX (and hard to convert to anything other than a printed page). Many Journals, even if accepting TeX from authors (to make it easy for author submission) put the documents through complicated and error prone conversions to internal SGML formats (or in some cases simply printed the documents and had them re-keyed in those formats). Having an open widely available format like MathML allows the tooling around an XML/SGML Math markup to be more easily shared (and improved).
MathML (rather than TeX) is part of the EPUB standard for electronic books, the DAISY standard for audible/accessible electronic publication, and part of HTML5. It underlies the Math formatting in OpenOffice and other ODF based office suites and it is supported as cut and paste of mathematical expressions in MS Word and the Math input panel. MathML doesn't compete with TeX in any of these areas as TeX simply was was not considered, primarily as it is just too "different" to fit into workflows that are not totally designed around the TeX processing model.
Conversely when it comes to typesetting MathML, TeX is still probably the best mathematical typesetting system there is.
Probably I should mention in case it isn't obvious, that I have various conflicts of interest here, as a member of the latex3 team responsible for LaTex2e and an editor of the MathML specification, so these comments can't exactly be considered an impartial review
Besides being a great format to mark mathematics and the production of outstanding output, some other reasons as explained by arxiv.org a heavy user of TeX\LaTeX.
TeX has many advantages that make it ideal as a format for the archives: It is plain ASCII, it is compact, it is freely available for all platforms, it produces extremely high-quality output, and it retains contextual information.
It is thus more likely to be a good source from which to generate newer formats, e.g., MathML [namely HTML, or more specifically XML, that handles mathematics correctly -- note that the MathML people plan a LaTeX to MathML translator, but dvi/ps/pdf lack the necessary document structuring concepts]. Possession of the source thus provides many additional options for future document migrations. Using emerging new technology, most of the Postscript generated from the source contains hyperlinks, so that using new versions of PostScript previewers (e.g., the next version of Ghostscript/Ghostview), readers can point-and-click to navigate within the paper, and even over the web itself.
And by archiving the source, we maximize the potential for seamless adoption of future technological improvements. Archived papers can be repeatedly rejuvenated by automated reprocessing.
Simply put, it does a great job and fulfills the requirements of its users.
Leaving aside the power and flexibility of LaTeX, the huge existing codebase coupled with the lack of good conversion tools is a currently an insurmountable obstacle to any move away from LaTeX. I teach university mathematics. Like most of my colleagues, I maintain several hundred teaching related LaTeX documents (plus many other research documents). I would dearly love to be able to generate html pages with MathML equations from the LaTeX source seamlessly in a way that:
At present, this is all a dream. Even if good conversion tools existed, the lack of browser support for MathML means few mathematicians would even contemplate publishing anything this way. So we are stuck with publishing materials in pdf format on web sites, with all of the downsides that entails. So in university mathematics and engineering departments, I would say LaTeX is unlikely to yield much ground in the near future. Anyway, I thought that the perspective of a major and influential segment of the LaTeX user base might be of interest.
As for comparing Word with Equation Editor to LaTeX, well, surely you are joking?
I would dearly love to be able to generate html pages with MathML equations from the LaTeX source seamlessly you can try tex4ht.