Do unused functions get optimized out?

It depends on the compiler. Visual C++ 9 can do that - unused static functions are removed at compilation phase (there's even a C4505 warning for that), unused functions with external linkage can be removed at link phase depending on linker settings.

MSVC (the Visual Studio compiler/linker) can do this if you compile with /Gy and link with /OPT:REF.

GCC/binutils can do this if you compile with -ffunction-sections -fdata-sections and link with --gc-sections.

Don't know about other compilers.

As a general rule, the answer is:

Yes: for unused static functions.

No:   for unused globally available functions.

The compiler doesn't know if some other compilation unit references it. Also, most object module types do not allow functions to be removed after compilation and also do not provide a way for the linker to tell if there exist internal references. (The linker can tell if there are external ones.) Some linkers can do it but many things work against this.

Of course, a function in its own module won't be loaded unnecessarily by any linker, unless it is part of a shared library. (Because it might be referenced in the future at runtime, obviously.)

Many compilers do, but it depends on the particular implementation. Debug builds will often include all functions, to allow them to be invoked or examined from within the debugger. Many embedded systems compilers, for reasons I don't totally understand(*), will include all of the functions in an object file if they include any, but will omit entirely any object files that aren't used at all.

Note that in languages which support Reflection (e.g. Java, C#, vb.net, etc.) it's possible, given the name of a function, to create a reference to it at runtime even if no references exist in the code. For example, a routine could accept a string from the console, munge it in some fashion, and generate a call to a function by that name. There would be no way for a compiler or linker to know what names might be so generated, and thus no way to know what functions may be safely omitted from the code. No such difficulty exists in C or C++, however, since there is no defined way for code to create a reference to a function, variable, or constant without an explicit reference existing in the code. Some implementations may arrange things so that consecutively-declared constants or variables will be stored consecutively, and one might thus create a reference to a later-declared one by adding an offset to an earlier-declared one, but the behavior of such tricks is explicitly not guaranteed by the C or C++ standards.

(*)I understand that it makes compiling and linking easier, but today's computers should have no trouble running more sophisticated compiling and linking algorithms than would have been practical in decades past. If nothing else, a two-pass pre-compile/pre-link/compile/link method could on the pre-compile/link phase produce a list of things that are used, and then on the "real" compile/link phase omit those that are not.

With gcc if you turn on the optmizations it can remove unused functions and dead code.

More on gcc optimizations can be found here