Here’s the object in Unity 2.6:
And here’s the same model, same wood texture, same material, in Unity 3.3:
What the hell happened!? And more importantly, how do I fix it?
It looks like your normals are screwed up. You could try changing the normals generation from “Import” to “Calculate” in the importer options. The proper place to fix this would be in your modeling application, though (make sure that all the normals are pointing in the correct direction).
What software are you bring this model in from? It could possibly be an exporting issue; Unity should be using the same exporter regardless of version but maybe exporting an FBX file manually from your 3d software will get you a better result. The screenshot kind of makes it look like you have two copies of the mesh sitting on top of each other; another possibility is if the file you are importing from has something like a hidden copy of the mesh (or, in Maya at least, an extra transform node from something like a boolean or mesh combine operation), Unity will import the hidden object as an extra visible one.