I've seen it used for prototyping, proving and equation simplification in the simulation space, but then those algorithms were converted to C++ for production use.

MATLAB can also be used in this fashion: http://www.mathworks.com/products/matlab/

I know an engineer at Boeing who leans on it heavily for his research. I'm not sure exactly what his department/responsibilities are, but there's one data point anyway.

I work at a biotech startup in the bay area and we use it heavily. Every piece of scientific data is parsed, analyzed, and shared in Mathematica.

I use it for prototyping, analyzing data, and explorative research. When considering a new approach to a computational or machine learning problem, you can often try it out in Mathematica and see if it's the right direction at all.

From what I've observed, Matlab is more popular. There's a perception -- for whatever reason valid or invalid -- that Matlab is for numerical computation, and Mathematica is for symbolic or higher level math. And, that Matlab is easier.

However, I'm noticing a trend towards using mainstream programming languages and whatever free libraries are available, to do the same kind of work. I used Mathematica 15+ years ago, and for doing the same kind of work today, I now use Python and am quite happy with it.

I built some utilities with it, like a Wheatstone Bridge calculator, that I use sometimes when I'm doing electronics.

I know several industrial physicists who use it very heavily.

Excellent platform for fractal research. And trust me not all of those who search are academics :)

It and MATLAB are popular in finance.