Advice regarding editing careers can be tricky. I've seen numerous posts discussing the subject, and several comments regarding which degree to pursue. Those commenting often suggest studying English. However, I would suggest an alternate path. Although it is possible to obtain an editing position with a degree in literature, creative writing, or another similar subject, you will likely be limited in what you can do with it. Not only does editing take a great amount of skill in grammar and the basics of good literature, but it takes training in technical writing, plot/character development, and the publishing industry in general, as well as experience in style and flow of prose. Depending on the types of documents you edit, a background in other fields might also be necessary. Being able to monitor consistency and accuracy of information is a must.
So what is the best option? That depends on the specifics of where you want to work, what type of editing you wish to do, and your personal strengths. First, focus on a major that will teach you as much as possible about English and writing while still giving you a variety of skills. One area of study I always recommend is professional writing. It's a major that teaches you things such as critiquing methods, writing in groups, peer editing, review writing, knowledge of the English language (including grammar), technical writing, how to be concise, and a bit of web design. Plus, if you can minor in a few non-related subjects on top of a major like that, you have even more of a competitive advantage.
Professional writing was the right major for me. I was able to pursue a degree in that while obtaining minors in German and psychology. I also took several classes in science, math, and creative writing. That experience gave me the opportunities to hold positions in technical writing (both for a medical company and for welding companies), document design, copy editing, substantive editing, developmental editing, web design, and other similar fields. I was able to work in a variety of environments and discover which paths I enjoyed the most.
That's not to say English degrees are useless; they do have their merits. English majors usually do a lot of reading and discussing what they read, which can really help you learn about different styles of writing and the pros and cons to each. But I think there are additional options available for those looking to go into editing full-time. Professional writing and technical writing both include their fair share of reading, particularly if you minor in (or take classes) in similar fields.
Additional resources: If you haven't yet read This Crazy Industry's post about becoming an editor, I highly recommend it. The blog covers the types of editing as well as suggestions for ways to get there.
Edit: This article was updated with further information.