Update: Now (2013) Clang is ready for prime time and used by some companies like Google. However it is not totally usable on Windows, work on this platform is a "work in progress".
LLVM/Clang is currently the default compilator on MacOSX/XCode but it's not exactly the same releases than the LLVM ones so beware of the minor differences (mostly difference of version numbers).
Well following the clang dev mailing list, recently the trunk version have been successfully building :
- the linux kernel (a recent revision)
- Qt (with it's special build process too, apparently)
- Chromium (a recent revision)
So, I would say that the coming version (2.9) might be a good "ready for prime time" compiler.
However, if your project have a a planning and budget, maybe it's not a good idea to try a compiler that isn't heavily tested yet. If you're allowed to experiment and provide feedbacks to the Clang developers community, then go for it, it's win-win for everybody.
If not, maybe you should use a mature-and-heavily-used compiler like gcc (in its recent versions) to have a "stable ground" to rely on while working on your project.