Three.js r120 was just released with the first version of a 3DMLoader which uses the rhino3dm.js library. The three.js editor also supports loading rhino 3dm files.
The first version was focused on getting all of the mechanics of loading rhino3dm.js in place and converting some important types like BREPs, Meshes, Extrusions, Points, Point Clouds, Curves, Dots, and Lights. Blocks are also supported, but do not take advantage of instancing (yet). There is also basic material support.
In the next version there should be support for more complete materials, textures, and a revision of the object conversion.
The easiest way to try this is to point your browser at the three.js editor and go to
File->Import and select a Rhino file. If the Rhino file has no lights, I recommend you add a Directional Light in the three.js editor (