What is the name of this common metal tubing?

Structural aluminum extrusion:

http://www.8020.net/

http://www.minitecframing.com/ (my favorite)

http://www13.boschrexroth-us.com/framing_shop/

T-Slot is the name I recognize it as. I assume there are also generic T-slotted aluminum extrusions available as well.

While you're probably looking at "full size" structural extruded aluminum T-slot, for completeness I'm going to mention miniature versions:

MakerBeam is developing the Mini-T standard for open source hardware. http://www.makerbeam.com/

MicroRAX a light weight mini T-Slot building kit. http://www.microrax.com/