Mineways lets you export your Minecraft creations into files you can use for making images, movies, or 3D prints. It is a free, open-source program. You can create 3D prints on your own 3D printer or through a service such as Shapeways or Sculpteo, view your model on the web through Sketchfab, or render with Blender, 3DS MAX, Maya, Cinema 4D, or other rendering system.
NOTE: Mineways works with Minecraft "classic" (the Java version), up to release version 1.12.2. Mineways does not work with the 18x10b beta (and probably earlier betas), as the file format is being changed in a significant way. Once 1.13 is out I may update the file reader to understand the new format, but it certainly won't happen now, as the beta is very much a beta, e.g., many blocks are missing.
What's next? Go to the quickstart page.
Among other packages, you can export models for use in:
Rendered with Blender
3D printed at Shapeways
Shared on Sketchfab (click it!)
If you're wondering, Mineways is a hobby of mine, I don't make money on it (just the opposite). In this podcast I talk about why I made it. Short version: for fun! My payoff is seeing what people do with Mineways, so please do send me pictures of 3D prints or renders or movies you make.
Kids like Mineways, too. We've done 2-hour workshops about 3D printing at Parts & Crafts in Somerville, Mass. - here are the presentation slides. I've also presented at Minecon 2016; here's my report, slides, and talk.
BTW, secret tip: click at the top of this page on the teapot and you'll cycle through all Mineways documentation pages.