Going back two years there has been work to build the Linux kernel with LLVM's Clang C/C++ compiler and then as of earlier this year a more concerted effort to building the Linux kernel with Clang -- that work was led by Qualcomm's Innovation Center but emerging since have been i586 and x86_64 targets in addition to ARM. For centralizing these resources there is now the LLVM Linux kernel Linux Foundation page that collects the necessary information and patches for building the Linux kernel with the Apple-sponsored compiler rather than GCC.
Aside from the direct work being done to allow Clang as a viable compiler option for assembling the Linux kernel, there's also been the Debian project that's been decoupling GCC from the Linux distribution so that LLVM/Clang can build most Debian packages. Within FreeBSD they have now switched to Clang and deprecated GCC with their compiler and other core packages already being in good shape.
Another distribution that's been toying around with the idea of building their software with Clang is Gentoo. Going back to earlier this year there's been this Gentoo bug tracker for the support of LLVM/Clang as an alternative system compiler. "LLVM/Clang seems to be the future as far as open source compilers go. The FreeBSD developers switched to LLVM/Clang in FreeBSD 9 and the Debian project appears to be considering a switch as well...It is probably a good time to look into building Gentoo with LLVM/Clang. FreeBSD upstream has already switched, so this should work well for Gentoo/FreeBSD. With some work, this could be leveraged by Gentoo Linux and Gentoo Prefix as well."
Most of the bugs blocking this have been packages hard-coding their CFLAGS and GCC compiler dependence and then the expected failure of some packages failing to build correctly with Clang instead of the GNU Compiler Collection. There aren't any plans for Clang to unseat GCC within Gentoo at this time, but the point is to make Clang a viable compiler option.
With the new LLVM Linux x86_64 target, benchmarks of building the Linux kernel with Clang are forthcoming on Phoronix.