Non-computational software useful to mathematicians
I like Asymptote for making pictures.
This is my short list of math related software not used for computing. I made an effort to list software in descending order with respect to the frequency of use. I left out $\TeX$ and my version control system of choice CVS since OP was not interested in those.
A good editor. My choice goes to nvi.
A spell checker like ispell.
Regular expressions for pattern matching/search.
Make utility.
I do not know about you guys but for us who must teach and manage grade books nothing comes close to being as useful as awk.
A good file synchronizer like Unison.
Shell script(sh).
sed.
An e-mail client like mailx.
PostScript language as a page description language for printing but also a tool for teaching geometry classes. Obviously you must have PostScript interpreter on your computer like GhostScript (comes with a viewer) and a good PS manipulation tool like psutils.
A tool for manipulation of PDF files. I like Pdftk.
Python as a glue language and for instance its library Matplotlib for making illustrations.
A good image processing tool like Graphics Magic.
Vectorial drawing program as Xfig.
I like IPE for quickly drawing figures, especially if you want to add TeX/LaTeX.
(Also see: The IPE Wiki)