Mathematica is one of the most impressive pieces of software I’ve ever used. I use it any time I can find an excuse, which is unfortunately not that often (it’s surprising how rarely math intrudes upon the actual day-to-day life of the software developer).
In line with its professional utility (my brother-in-law uses it when designing electromagnetics for FermiLab), Mathematica costs a pretty penny. However, Wolfram Research has just released a \$295 version for non-professional use (Mathematica 7 Home Edition). Not exactly cheap, but when I specifically asked if it was limited, I was told it is “a fully functional version of Mathematica Professional with the same features.”