I have been able to build LLVM 2.6 (the llvm-2.6.tar.gz package) using MinGW GCC 3.4.5. I haven't tested properly, but it seems to work.
The trouble is, I have libraries of my own which don't build using GCC3, but which work fine in GCC4 (template issues). I believe the first official GCC4 version for MinGW is GCC 4.4.0.
EDIT
Decluttered - everything useful in the "tried this tried that" info is now in the answer.
EDIT
Most of this question/answer is redundant with LLVM 2.7 - the standard configure, make routine works fine in MinGW with no hacks or workarounds.