Taking courses beyond requirements in a Ph.D. program
As an adviser, I encourage my graduate students to take classes they find interesting and/or that broaden their knowledge and therefore are useful to later finding jobs. Ultimately, my goal in this is to help my students become well rounded and broadly educated graduates who will be successful in life. The only caveat I place on this is that they need to make sure they have enough time to do the research that will ultimately lead to their thesis and their defense.

I don't know whether I'm typical in this, but would imagine that most advisers will agree to let their students take other classes if a student asks and gives a reasonable justification. I think most will even agree to this if the student is paid from a grant.