One of the contradictions of being a math professor is that a big part of your job is to train people to do things which are quite different from what you do yourself professionally; this is especially true for undergrads, but to some measure also with grad students.
This is not particularly helpful when it comes to convincing students that they should major in mathematics; most mathematicians I know, myself included, are quite ignorant of what people will actually do if they get BAs in mathematics, and don't go to graduate school, or otherwise enter education, which is obviously something students will be very concerned about in these tough economic times.
Obviously, the correct response is to educate one's self on what the job opportunities are for people with BAs in math. I'm mostly interested in the US context, but would be happy to hear about other countries as well.
The best resource I know is the AMS Early Career Profiles page. This is a lot of links (some broken) to profiles of BA graduates in math that individual departments have put together. There some other reasonable links on this website. Is there anywhere else I should be looking?
Best Answer
My experience, based on years in and out of academia, is that both students and professors vastly overestimate the connection between a major and a career. If you speak with successful professionals 20 years after their college graduation, you find that their majors are really kind of random. Among the people I talked with today, for instance, were a super-talented programmer who majored in English, a tech entrepreneur who majored in graphic design, and marketing executive who majored in philosophy.
I think the best advice for a student is to major in a subject that they'd enjoy studying for four years. That way they'll have a good time and find it easy to work hard! Note also that "enjoy studying" means the whole process, taking into account which subjects have inspiring professors and interesting fellow students.