You can't go wrong with writing, as it is nearly universally required and will be among the last skills to be Turing'd. A STEM major who can write well is a scarce commodity, if the GRE scores are any indication. (I would not recommend taking a course to improve your writing however. Just start writing a blog or something. And read Eats, Shoots & Leaves.)
If you have trouble socializing, learn how to do that. Most jobs opportunities come through socializing. Even the jobs that are advertised still require a competent interview.
Colleges have a breadth requirement; one source I read suggested using that to take a writing heavy course in history or philosophy that requires lots of short papers in order to improve your writing.
To further elaborate the question: What are the most universally and most useful skills one could learn at a university? Currently, I am studying physics as an undergraduate and I am thinking about my career options. I have gotten opinions in other forums as well but I would really like to hear your thoughts and I also think that other LessWrongers would find such a list useful. To give you a rough idea of what I mean I have two examples:
What are some other skills along this line that are universally useful?