If you learn carpentry or programming you have the clear options of becoming a carpenter or programmer. But what if you learn mathematics? I know that there are some financial institutions out there, who are in need of hard core mathematics, yet I don't know exactly how to ensure a position in such a place, or how does the prospect of this institutions look like in the coming years. What kind of mathematics I should learn, if I want to maximize my chance of finding a relevant job, and by relevant, I mean related to mathematics, say geometry.
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A research student from Bangor went in to industry, and he wrote to us: "We can get as many computer scientists as we want, but a mathematician who can say which area of mathematics is appropriate to the problem at hand is worth his weight in gold!".
One of our graduates visited us from joining a software firm, and I asked him what course he found most useful to him. To my surprise he replied: "Your course in analysis, as it gave me an idea of rigour."
See also Why study mathematics?.
From the perspective of somebody still on an academic career path (so hopefully people with other perspectives will weigh in as well), what makes you widely employable as a maths graduate are the analytical skills and problem-solving abilities you develop by using them a lot to do mathematics, not the actual content.
Certainly there will be jobs that use certain pieces of theory, but you aren't always (maybe even often) required to know these inside out before you start, as long as you've proven your ability to get to grips with mathematical concepts.
My advice would be to follow your interests instead of having a specific career in mind. It'll be very difficult to avoid learning something that makes you employable, and this way you make sure that your skills and interests align to some degree.
This is possibly a naïve view (although it is based on the successful path to employment taken by a lot of the people I graduated with), so I'd be interested to see if other people have different (even contradictory) answers.