Word processors are getting better these days, and I'm wondering if LaTeX was a solution in the past for a buggy Microsoft Word, and it programmatically gave you the options to do formatting. I'm just starting out with LaTeX, and I find it quite good. I don't want to be working or learning an outdated technology (if it is).
There are three aspects.
The first is the superior typesetting that LaTeX delivers. As long as no word processor approximates LaTeX’ algorithm for paragraph breaks, the latter will have its place in producing professional layouts.
Just compare a page of text written in LaTeX and Microsoft Word (or any other word processor) in the same font. The LaTeX-set text will look far superior because it will be more evenly distributed on the page, use word breaks more judiciously and if microtypography is enabled this will even have a stronger effect. There is simply no question that LaTeX delivers something unique here.
LaTeX cannot be replaced by a word processor here, only by a DTP (desktop publishing) system. Modern DTPs exist but are prohibitively expensive for most people.
The second is mode of operation: in LaTeX, I program my documents. This is fundamentally different from the usage of word processors or “modern” DTPs. But it’s not necessarily inferior.
Quite the opposite: I’d argue that it’s superior once you have learned the basics because it will always be vastly more powerful and faster to use. In fact, modern word processors provide complex scripting engines (VBScript) with huge libraries to allow users to automate certain processes. Most of what these engines offer comes for free in TeX and is vastly simpler to use.
The third is modernity of underlying technologies. Here LaTeX has some weaknesses compared to other systems and programming languages. TeX is pre-Unicode and the Unicode support that was grafted on is still causing trouble. Likewise, TeX lacks almost all features of modern programming languages. Foremost among these is the lack of a good module system. This makes package writing really painful.
In all these aspects LaTeX is indeed woefully outdated (although it gets better with XeTeX, LuaTeX and LaTeX3). But as long as there are no alternatives, TeX remains the only choice.
A question like this is of course open to discussion, and all I can offer here is mo own personal opinion and experience, but IMHO TeX is definitely not outdated.
It is true that word processors are getting better and better, and as they develop they will implement more and more features of TeX. In fact, TeXmacs implements most of the typesetting algorithms TeX does, and you can create certain type of documents in it that are impossible or nearly impossible to recognize from documents created by TeX.
The problem for me is all these tools lack the flexibility and extensibility of TeX. If I want to create a new type of document, or change a look of an existing one, it is relatively easy to do in TeX. I can create new document class, or write a simple or not so simple package, and then I can use it over and over again. Some word processors are also extensible and programmable, TeXmacs for example can be extended in scheme, but you have to learn another language to do that, while in TeX you use the same language to for the extensions as for the actual document, which I believe makes it much easier. Just compare the number of different packages for TeX with the number of plugins for TeXmacs, or layout files for LyX. I generally find word processors very limiting when trying to do new things.
Other great advantage of TeX for me is the fact that I can do all my editing in the same text editor I use to write code.
There are many things about TeX that could perhaps be done better, especially now when we have much more computing power, memory and other resources available. TeX may be eventually replaced by another programmatic system, that will perhaps use a more powerful or more mainstream programming language. Any such system, however, will have an uphill battle to fight, as it will have to replicate huge number of existing TeX formats, modules, document classes and packages, as well as existing TeX development environments (one reason I am not using ConTeXt more is that there is no equivalent of vim-latex for it. Now imagine a completely different language.)
In addition to all that, there is fairly good amount of active development going on in TeX, with new engines (XeTeX, LuaTeX), formats (ConTeXt, LaTeX3), powerful packages (for example pgf/tikz and related tools).
One big factor in the future-proofness of TeX is its use in the academic environment. The apprenticeship of young scholars under established ones passes down not just the scientific methods but the technological ones. I realized this when emceeing a recent undergraduate mathematics research symposium. The talks in more biological fields were done in PowerPoint, but the ones in theoretical physics, combinatorics, knot theory, etc., were in LaTeX beamer. Between talks I remarked that it was good to see TeX is safe for another generation.
All answers so far are good reasons to continue using TeX. One advantage not yet mentioned (and which will no doubt be seen as a disadvantage by many individual users) is the fact that it is batch-oriented, and reliably generates the same output from the same input in successive iterations. Hence it is admirably suited to production use for a technical publisher, in particular for journals. When authors submitting manuscripts to such a publisher have followed the publisher's guidelines and used the provided document classes, errors and misunderstandings are minimized and the resulting publication emerges faster and more accurately than when using other tools.
Technical typesetting is such a small niche market that it has always been called "penalty copy". Nobody is going to make a financial killing by developing a commercial tool, so the incentive to do so is very low.