OK. So I thought I had this licked ... but now ....
I have a project which includes one small library from GitHub as a submodule. In the original version of that super-p
I had the same issue with a submodule on a project. When I tried to clone the submodule separately it worked well.
I've tried all of the answers above, but without success (git submodule update, ..., removing the submodule folders, ...).
The issue disappeared after update of git (from Git-1.7.11-preview20120710) to latest version (to Git-1.8.1.2-preview20130201) at the time. Strangely my colleagues had even older version, worked without any issues, but they were on Mac. I'm on Win7 64bit.