Over the holidays I had a chance to talk with one of my cousins who just got home from his mission and is back in school, but doesn't know what he wants to major in. (We've all been there, right?) Sure, he'll minor in his foreign language, but he doesn't really have anything in mind other than that.
He didn't ask for my advice and I didn't offer any, but having been in that situation myself, I feel like I have something to offer that could be valuable to someone out there. At least I know what I would do differently if I could go back and do it again.
The short answer is this: Major in accounting.
It's simple really. BYU's accounting program is consistently ranked in the top five in the nation, often taking the top spot. As long as you're at BYU primarily for reasons having nothing to do with academics (value, environment, to get married) why not get the most marketable degree they offer while you're there? It works on it's own or as a foundation for med school, law school, etc. If BYU's electrical engineering program was the best in the nation, I'd recommend it for all the same reasons.
The long answer is from Paul Graham: stay upwind, solve problems, and follow your curiosity.