Free and open-source computer-aided design/What exists already?
There are some two-dimensional (2D) open-source CAD programs such as QCAD. These really only replicate the methods that were used to create hand-drawn engineering drawings so lack the advantages and power that modern 3D modelling offers.
BRL-CAD is an 3D CAD package that came out American Military ballistics research and can be traced back to the 1970s. It is based on the older constructive solid geometry paradigm that isn't as flexible as the parametric b-rep software used by modern proprietary CAD programs, although very suitable for physical analysis, which is what it was designed for. The user interface and experience is rather lacking.
Blender is a powerful 3D modelling, animation and rendering program designed primarily to create sophisticated computer graphics rather than being tailored for design and engineering. It is an advanced and capable piece of software, and might well form a good basis for a dedicated open-source CAD application – such are the possibilities when the software is open-source. The user interface is not known for being particularly intuitive, however those that know their way around it (including the many vital keyboard shortcuts) say it is very effective.
Art of Illusion this is another interesting open-source 3D modelling and rendering application, although perhaps not quite as advanced as Blender. Similarly it is designed for creating computer graphics rather than as a CAD program, but the required features could be added. The RepRap open-source 3D printer project are currently using this for their 3D modelling with some additional scripting.