WHAT COULD I DO WITH A DEGREE IN MATH?
If you want a list of practical reasons to major in mathematics (including stats on average starting salaries and comparisons of LSAT and GMAT scores across undergraduate disciplines) check out this link from Duke University.
If you're convinced getting a degree in math is worth it, but want a list of various occupations where a degree in math would really come in handy (not necessarily within the academia track, and specifically including jobs that do not require graduate work AT ALL), check out this link from weusemath.org.
If you want to become a mathematician, you're going to need to go to grad school and realistically you'll need a PhD. But, if this is the route you want to take, you should first know the answer to the question "What exactly do mathematicians DO all day?"
If you'd like to know what the U.S. Bureau of Labor and Statistics thinks, here's how the government defines a mathematician.
If you want to hear it "straight from the horse's mouth" (so to speak), the Mathematical Association of America (MAA) has a link which in turn discusses resources about being a mathematician specifically written BY mathematicians (there's a section on being a woman in math as well).
If you're looking for things to do with a PhD in math that are non-academic in nature, while exact digits are (of course) classified the National Security Agency is historically one of the largest employers of mathematicians.
WHAT NON-MATH SHOULD A MATH MAJOR CONSIDER LEARNING?
(Computer) languages: in this day and age, the better you are at coding, the better your job prospects will be. This is certainly true if you want a non-academic track and is increasingly true if you want an academic job. If you want to get your feet wet with programming, I highly recommend codecademy. All you need is an email address and an internet connection and you can start to learn html, java, and python (which is good to learn if you'd like to use Sage, which I highly recommend you use).
(Human) languages: many graduate programs still ask you to pass (written) language exams--though it is becoming less prevalent. The traditional three foreign languages for math are French, German, and Russian. Italian may also be an option depending upon the program. Certainly knowing these languages will not hurt you--there are many historically important papers which have not been translated. If you are in the process of translating a math paper in one of these languages, I have found the following links to French math vocab and German math vocab to be life-savers (i.e., better than google translate!).
Economics/Business: If you want to become an actuary, or work on Wall Street, or anything of that nature, you'd be crazy not to learn more about basic economics and business. Just look at the topics for the actuarial exams. It is increasingly common for economics students to double-major in math; it's historically common for business majors to minor in economics. If you're a math major who wants to enter the business/econ world, minor or double-major!
*If you have any information you'd like me to add to this page, please email me. You have my thanks in advance.