Paul Harter of London has created Printcraft, a web site and pair of Minecraft servers that allow players to 3D print their Minecraft creations.  Those with Minecraft accounts can log into one of the Printcraft servers, build something in a building plot, then press a Print button, extracting the game model into a Printcraft Window for downloading, sharing or printing as an STL file.

Printcraft has teamed with Thingiverse for sharing and i.materialize for individuals without 3D printers of their own.  These options are directly available in the Printcraft Window.  The Printcraft server addresses are eu1.printcraft.org and us1.printcraft.org.