First off, UX and UI is not the same thing, so what degree you pursue is directly related to which one you want to focus on. User interfaces are the predominant canvases that user experience designers use, but if you focus on user experience as a discipline you don’t necessarily need to be good at interface design. I’ve worked with some great UI designers who weren’t very good user experience designers, and fantastic user experience designers who couldn’t create a usable UI if a gun was pointed at their head.
So… If you want to focus on user experience design, I suggest you look at psychology as a major, and a minor in technology. If you want to look at UI design, I’d consider a graphic design major with a minor in psychology. That being said, there are amazing UX people who come from many varied disciplines and have dozens of different degrees (I majored in journalism, myself), so I recommend looking at college as an opportunity to learn as much as you can about multiple disciplines.
Speaking of disciplines, a core discipline in both UX and UI is problem-solving, so if you can get a couple of classes in philosophy and logic it’ll help. Finally, many majors in Information Technology are very well-rounded and have many of the classes that would benefit someone looking into breaking into the field, so that’s something to consider as well.