how about someone that enters, let's say, a chemistry program, thinking he could be a chemist after college, and right when he graduates, he has a change of heart and wants to do something else? is his chemistry degree now useless because he didn't get rich off his major? perhaps he learned something about himself that made him incompatible with the field. that doesn't mean all of those years studying chemistry were useless because he's not in a job related in it. in fact, you can argue that he needed to study chemistry to find out what else he can do instead of chemistry based on the skills acquired in the chemistry program.
But that's personal reason, and not related to the degree. A chemistry degree is useful for reasons X, Y, and Z. If someone graduates from Chemistry and doesn't like the field, it doesn't change the usefulness of the degree itself. It only changes the usefulness of a chemistry degree for himself/herself.
If the topic is, "What are the most useful degrees?", I'd still go with mechanical engineering, electrical engineering, or computer science.
If the question is, "What are the most useful degrees for someone whose interests include A, B, and C", then that's different. I mean, if you're interested in acting, then obviously chemistry is useless to you. However, you can't really ask the question presented to us and then base your answer off your own personal interests. The answer must be objective, and leave ones own interests behind.
The question requires us to treat degrees as a Swiss Army knife. For general, practical, day-to-day, "take anywhere" and "do anything" degrees, mech eng, electrical eng, and computer science are useful degrees, even if they're not useful for what I want to do in my personal life. They're clearly not related to cancer treatment; however, I'm certain my degree isn't the most useful degree once I leave the university/hospital/research lab. In our technological world, computer science would help. Same with mech or electrical engineering.
2. I have no interest in "breaking into" the engineering or corporate world, so why in the world would I study something that would make the rest of my life miserable? Because I'll make money? Not for me. I suppose we have different priorities in life, but happiness comes above wealth, for me.
3. I do have foresight. Seeing as how after I graduate, I'll be going to grad school to study History, my B.A. in History won't be a "waste of time".