Depending on your career path, advanced degrees tend to open more doors for those that just graduated, and allow for higher pay rates than their colleagues who may not have the same credentials.

I don't think degrees have any correlation to "intelligence"....it just demonstrates to employers that you are more dedicated to a specific subject matter, and/or you have the knowledge to be considered a "expert" in your field.

Only advice is don't pick a stupid subject matter to become a expert in..........

Yes, you can get a PHD in all kinds of subject matters these days, and many of these titles aren't worth the paper they are printed on.