From the Unity website
Unity can read .fbx, .dae (Collada), .3ds, .dxf, .obj, and .skp files. Refer to your 3D modeling software documentation for information about exporting 3D files.
I thought there was a QGIS plugin that exported extruded polygons to wavefront OBJ format but i can't find it :( Maybe it was my imagination, maybe it was withdrawn.
There is a plugin for Blender that imports shapefiles. This lets you
- create a triangulated mesh from contours shapefile
- load and extrude buildings from a shapefile
Once in Blender, you should be able to export to any of the Unity supported formats. Look on YouTube, there are some videos on there.
Another one in that list is .dxf , which can be exported from QGIS. I've not tried this, though.
It's a shame Stanford PLY (*.stl) isn't supported by Unity, there are a couple of ways of getting those out of QGIS (a plugin, and SAGA) although I think they're for terrain meshes.