This is a technique I picked up from Gregor Luetolf (gluetolf on Thingiverse). He details a very nice workflow for creating STL files from DEM data, but unfortunately (for some of us at least) Gregor, who lives in Switzerland, wrote in German. Google translate helps somewhat, but I thought I would explain this technique for the English speaking world along with a few refinements of my own.
The basic workflow is as follows:
1Acquire the DEM data
2Use QGIS to assemble, crop and convert the data to a .tif file
3Use 3DEM to convert the .tif file to a .dem file
4Use AccuTrans3d to convert the .dem to a STL file
5You can then use AccuTrans3d to solidify the mesh to facilitate printing, or you can do that later in Blender (or a similar modeler)
There are other ways of doing this, but this workflow works well and produces amazingly detailed maps. The great thing is that all of the software is free except for AccuTrans3d which is old-school honor system shareware with a $20 price tag. You get a 30 day clean conscience trial. The free trial never ends, but your clean conscience should. I bought it as soon as I saw everything it does.