I'm just getting started, and haven't actually used LaTeX for a real project yet...
I've had a few projects lately related to programmatically-generated documents, and I'm not satisfied with the results. LaTeX was on my radar, but I didn't had time to investigate until last week.
Some process complex lab data and produce a report that describes the results. Early versions were plain *.txt files; other than using a bit of white space they were difficult to read at times. Lately I've been using HTML output which allows for more complex formatting and is still accessible; but the output is inconsistent between browsers, and prints terribly!
I have also let the creation of some documents which were quote large and repetitive (over 2400 pages on 11x17!). Typically these documents are created by hand in Word, but that clearly wasn't an option due to the scale needed for these. We were able to generate MS Word files in sections, which were manually stitched together, and tweaked to keep it from breaking.
I have wanted to include diagrams, but haven't found a practical method of generating them.
At this point, LaTeX looks to be a great fit, as I can generate plain-text files easily enough (even broken across multiple files), then render them to print-perfect PDF files that anyone can view. With Tikz (or the like), I can even include those diagrams!