My answer is: TikZ
This is a programming language, often used in combination with LaTeX, for producing high-quality graphics.
I view this language as important for mathematicians, not because mathematicians will use it to solve their mathemaical problems, but rather, because mathematicians will use it to communicate their mathematical ideas to others. I believe that almost every mathematics paper would benefit from having more and better graphical illustrations, and TikZ output is often superb for this.
Here are some sample figures that I programmed in TikZ for some of my recent work, including research papers and expository work. I am just a beginner, and I am sure that there are other users on MathOverflow who are truly expert. For example, Joseph O'Rourke is a master of graphical presentation, and my impression is that many of his figures might have been created with TikZ. I would expect that he can provide some inspirational examples.
