Objective-C can be compiled and run on Windows, Linux, *BSD (ie. FreeBSD, OpenBSD and NetBSD), Solaris and Mac OS X.
You can run it on iOS Devices. You can't build it but must cross-compile on Mac OS X.
There are two compilers - GCC and clang/llvm. Apple's Xcode comes with clang/llvm, for the others one uses gcc.
There are three main things you need: the compiler, the runtime and the libraries.