Mineways is a free, open-source program for exporting Minecraft models for 3D printing or rendering. You don't need a 3D printer, you can easily upload and view (for free) and buy models using 3D print services. You need the world to be saved on your computer, running Windows, Mac, or Linux. You interactively select a model from a world map, which creates a 3D print file. Preview this file with MeshLab or other 3D file viewer. Send it to your own 3D printer or a 3D printing service to make the model real. See the step-by-step guide or the two-minute introductory video for the whole process. Prices of 3D prints range from $5 to $500, depending on size - my mantra is "smaller is cheaper, cuter, and cooler". Or, just enjoy viewing and rendering your creation in a different way (but for rendering you should probably be using jmc2obj).
The latest version for Windows is version 3.06, for Mac it's 3.05. Read the notes for the Mac - it's a bit tricky to use. For Linux, use WINE to emulate Windows. All versions work with Minecraft 1.2 and later. Mineways Version 1.15 works with Minecraft 1.1 and earlier, though I find it easier to just convert old worlds by loading them into Minecraft itself.
Kids like Mineways, too. We did a workshop at Parts & Crafts in Somerville, Mass.; here are the presentation slides. We'll be demoing Mineways at the Cambridge Science Carnival on Saturday, April 17, 2014. If you're wondering, Mineways is a hobby of mine, I don't make money on it (just the oppposite); in this podcast I talk about why I made it.