Some resources I like.  This isn't a complete or impartial survey at all – the field is too big for me to try that now – just some links from me personally.

Software

Rhinoceros 3D CAD modeling software.  Not the shiniest at anything, but it has capability in both NURBs and mesh modeling, as well as strong scripting and support for many file formats, all of which make it easy to interface with other software.  No one tool can do everything I want, so my wheelhouse is the tool that plays well with others.

Surface Evolver Freeware for studying and creating minimal surfaces, relaxing knots, and many other things that are over my mathematical head.

Qhull Mathematical freeware for computing convex hulls and Voronoi networks.  Again, much of what this does goes way over my head; but I can report that the parts which I can understand work well.

Chaoscope Ineffably gorgeous strange attractors.

SeifertView A tool for generating and visualizing Seifert Surfaces.

TopMod A topology-based mesh modeler.

The net is littered with tools like these, single-purpose utilities written by and for fans of particular concepts.  I love them, but I can't begin to mention even all the ones that I've used.  They vary greatly in documentation and ease-of-use.  They're like unexpected windows in the cathedral of mathematics.

Mathematica This comprehensive tool needs no introduction, but I want to mention that it has the ability to write STL files, which is the standard format for 3D printing.  Much could be done with this.

Maxwell A renderer which purports to simulate the physical properties of light.  It has settings like an SLR camera and specifies materials by their optical properties.  It is extremely slow, but the only renderer I've ever managed to make any sense of.

Materials

Shapeways This 3D printing service bureau, as of 2011, has won the Internets.  Great pricing on an wide material selection (including Prometal printing) is the crunchy shell.  Friendly documentation, the ability to sell designs to others, and a dynamic user community are the tasty, tasty filling.  If you're new to the field I recommend starting here; if not you may find competitive prices and selection here.  I rarely need 3DP parts other than metal, but when I do this is where I go.

Prometal, a division of Ex One Direct metal 3D printing.  I do most of my sculpture with this process, and the accuracy, freedom and strength of these parts is excellent.  Ex One is mainly an industrial/wholesale company, so not the place to get started, but if you have gained some metal printing experience at Shapeways or elsewhere, and now feel ready to have a direct relationship with the supplier, pick up the phone.

Reinmuth Bronze Studio A full-service foundry in located Oregon.  Steve Reinmuth is himself an extraordinary sculptor, and also a fantastic caster and finisher.

Treasures Mike Barajas, a full-service jeweler of great resource and technical prowess in Scotts Valley, CA.

Laser Crystal Awards High-end subsurface laser etching.  2D photos or 3D designs, quantities one to thousands, they can do it.

Crystal Sensations The best quality subsurface laser etching that I know of.

Math/Art

There is a great flowering of math/art going on.  My colleagues in this field are now legion, and Google tracks their doings better than I can, so I'll just mention a few of my favorites and friends.  Lee Krasnow and Oskar van Deventer's mechanical puzzles.  Vladimir Bulatov and George Hart, Princes of Polyhedra.  Paul Nylander and Torolf Sauermann's fantastic renderings.  Brent Collins and Bjarne Jespersen's credibility-stretching wood carvings.  Erwin Hauer and Robert Engman, great geometrical sculptors of the 20th century before technology was invented, and my fathers in art.  If you ought to be on this list and aren't, I can only say that it's not personal, there are just an awful lot of you! Two organizations that run annual math/art conferences, and have many artist and resource links:

Bridges Organization

International Society for the Arts, Mathematics, and Architecture (ISAMA)