These tools have been in use so far to create Exertion Instruments.  Please continue to fill them in:

Electrical

PSoC (Cypress) - Programmable System on a chip.  8-pin MCU with programmable analog and digital blocks.  DIP and SMD packages. 

QUCS - Free, open source circuit simulator.  Runs on Apple, Linux and Windows.  Simulates amplifier and power supply circuits.

Eagle PCB Editor - Schematic and Circuit board editor.  Very free.  Runs well on Apple, Linux and Windows.  Pay an upgrade if you want to edit boards larger than about 4x6 inches.

Programming

Cross Pack (Objective Development)  - Development environment for writing coding/programming on AVR/AtMega/ATTiny chips.  Mac version here.

Physical Construction

Machines That Make Machines - MIT CBA Project

Gear DXF - Generates gears well, but not gear racks.  For gear racks, get your hands on OMAX.  Windows only.

OMAX Layout Generates gears and gear racks well.  Windows Only.

Organizing

Bubbl.us - Online Mind Mapping software. 

Math

Octave - Free clone of MATLAB for Apple, Linux, Windows and others.  A very good number-crunching piece of software.  Has no graphics unless you install a second package.

R (Free, open source software) - Free clone of MATLAB for Apple, Linux, Windows and others.  A very good number-crunching piece of software.  Graphics modules available.

Open Office (F/OSS) - draws decent, simple graphs.  Good spreadsheet.

Web

These aren't favorites yet.  They remain to be evaluated.

Stack Overflow - A rundown of various graph layout (GUI for Max/MSP or PD) libraries for JavaScript

flare  -

Plot Kit  -

jsviz -

google's visualization stuff - lots of application-specific libraries, like gant charts.