I used it extensively in designing my side project synth[1], where I used its visualisation capabilities to figure out everything from panning algorithms to delay lines. It earned its keep most often late at night when I was tired and trying to figure out daytime-simple-but-nighttime-hard routines. The Manipulate[] function is really good for this, as it shows you the output of a function as you drag the inputs up and down. I also used it for turning mathematical formulae into C code - the CForm[] function does this very well.
It's also a great way to experiment with functional programming, since that's how it mostly likes to operate.
I reckon there's a lot of places you could use it, but it's too expensive to justify. I don't really care if it's open source or not, but I'd like Stephen Wolfram to have an epiphany on pricing and realise he could sell ten times as many Home Edition copies at a quarter of the price. Its adoption is absolutely held up by its sky high price.
Anyone with further interest in it should check out the Wolfram blog[2] and one of the friendliest StackExchange communities out there[3]
[1]http://www.omnivoresoft.com [2]http://blog.wolfram.com [3]http://mathematica.stackexchange.com
EDIT: Mathematica can do almost anything, but how do you use it actually in your work environment?
In particular I love to build up some complicated function of many variables and wrap a Plot[] command in a Manipulate[] command so that I can drag the slider bars around and see how the shape of the function changes. This allow for me to get an intuitive understanding of the problem.
On those rare occasions I need to solve equations or do some calculus, there's nothing better.
While this could be an extensive debate, I prefer Mathematica to Matlab whenever there is an option. I am a heavy user of both, though have never used Symbolic toolbox in Matlab. It starts a lot more complex in Mathematica, but becomes significantly more powerful shortly thereafter.