Windows 10 & Geforce GTX 870M
Broken: 2.78, 2.78a, 2.78-latest-build
When an edge of an ngon is beveled, it results in a strange mesh that is non-manifold. The n-gons on the side are attached to the wrong side of the bevel.
Exact steps for others to reproduce the error
This is the standard cube with the top face cut in two halves, with a couple of extra vertices.
Select the cube.
Tab into edit mode.
Make sure the edges cutting the top face is selected (nothing else).
Bevel them some.
Cube is now not manifold.