Free Tools for Engineering

FreeMat - much like Matlab http://freemat.sourceforge.net/
R - statistics processing http://www.r-project.org/
Blender - modeling, animation, video processing, compositing, simulations http://www.blender.org/
Portable Apps - apps that can go with you http://portableapps.com/ (Most are available separately)
*Notepad++ portable superior text editor
*Dia portable diagramming, like small Visio
*Audacity portable Audio recording and editing
*Windirstat portable Windows Directory Status - where'd the disk space go?
*FreeMat portable - like Matlab
*Blender portable - as above
*Speedcrunch portable - great calculator
*Camstudio portable - screen and audio capture
*LibreCAD portable - Like autocad
*Inkscape portable - like Adobe Illustrator
*GIMP portable - like Adobe Photoshop
LTSpice circuit simulation from http://www.linear.com/designtools/software/
Fritzing - Arduino development tool
EagleCAD - free for 2 layer small circuit board layout, like Arduinos
PTC Creo Elements/Direct Modeling Express - http://www.ptc.com/community/free-downloads.htm
CircuitLab - Circuit capture and simulation in browser https://www.circuitlab.com
AutoIT - for many Windows programming needs
Processing - software useful for animated graphics generation, and more http://processing.org

[Jibsy]

I can vouch for DraftSight. We use it at work for all of our 2D drafting. It's from Dassault, the makers of SolidWorks - it's their shot at Autodesk, essentially offering a free AutoCAD to complement SolidWorks.

[Nate Laverdure]

OpenOffice. Real engineering happens on a spreadsheet

Keuffel & Esser - Real engineering happens on a sliderule.

Fixed it for you.

Originally Posted by Nate Laverdure

OpenOffice. Real engineering happens on a spreadsheet

Forgot:

ProjectLibre http://www.projectlibre.org/ ProjectLibre: open source replacement of Microsoft Project. Gantt charts, resource availability, and more.

[Ether]

Maxima

Octave

SciLab

Graph

gnuplot

SPICE

AWK

[efoote868]

Python
Java

OpenRAVE

[Andrew Schreiber]

Originally Posted by Ether

AWK

SED? Honestly, without cat, sed, awk, grep, and xargs I wouldn't get my job done. I guess I could just say all of your usual *nix tools.

I'll second R with the caveat of RStudio makes things a lot easier to learn. (It's free)

[sanddrag]

HSM Express

[Eagleeyedan]

An amazing math tool, Wolfram Alpha