I have a texture mapped mesh, which looks normal in the 3D view, but when I run it in the blender game engine, something strange happens. Whenever there are two faces and one should be occluding the other, the furthest back face appears to be in front. Any ideas why this is happening? I've tried playing with backface culling settings and flipping mesh normals but none of that solves the problem.
It sounds like you enabled semi-transparency (alpha-blend/alpha-sort) at your meshes. This usually happens when you import the mesh from another format.
Switching off the transparency in you materials should fix the problem.