I know that the Name String on some AMD processors can be changed to return a different string. I believe the BIOS can disable cache or SSE support which would necessitate that the bits that indicate cache/SSE support would have to return different values.
Which values returned by the CPUID instruction are guaranteed to never change on a given CPU?
Thats incredibly generic, as CPU's tend to change over time and they differ between brands, you are better off using the CPUID manuals/specs from AMD and Intel, supplemented with the data from their respective developer manuals.
You'll probably find that the model and family related stuff is constant, along with a lot of the topological features.