Is a C++ compiler allowed to emit different machine code compiling the same program?

The C++ standard certainly doesn't say anything to prevent this from happening. In reality, however, a compiler is normally deterministic, so given identical inputs it will produce identical output.

The real question is mostly what parts of the environment it considers as its inputs -- there are a few that seem to assume characteristics of the build machine reflect characteristics of the target, and vary their output based on "inputs" that are implicit in the build environment instead of explicitly stated, such as via compiler flags. That said, even that is relatively unusual. The norm is for the output to depend on explicit inputs (input files, command line flags, etc.)

Offhand, I can only think of one fairly obvious thing that changes "spontaneously": some compilers and/or linkers embed a timestamp into their output file, so a few bytes of the output file will change from one build to the next--but this will only be in the metadata embedded in the file, not a change to the actual code that's generated.

There is no guarantee that they will be the same. Also according to http://www.mingw.org/wiki/My_executable_is_sometimes_different

My executable is sometimes different, when I compile and recompile the same source. Is this normal?

Yes, by default, and by design, ~MinGW's GCC does not produce ConsistentOutput, unless you patch it.

EDIT: Found this post that seems to explain how to make them the same.

According to the as-if rule in the standard, as long as a conforming program (e.g., no undefined behavior) cannot tell the difference, the compiler is allowed to do whatever it wants. In other words, as long as the program produces the same output, there is no restriction in the standard prohibiting this.

From a practical point of view, I wouldn't use a compiler that does this to build production software. I want to be able to recompile a release made two years ago (with the same compiler, etc) and produce the same machine code. I don't want to worry that the reason I can't reproduce a bug is that the compiler decided to do something slightly different today.