As an undergrad who has recently been looking for jobs I would make the following suggestions...
1) Learn to program! MOST of the jobs I've run into that require mathematicians/statisticians will eventually require learning one or more of Perl/Python/R/C++/SAS. I'm in the process of writing a book on the subject (programming for mathematicians, specifically in python)
2) Learn probability and statistics! I didn't do that directly and wish I had because I run into problems all the time for which probability and statistics knowledge would be useful.
3) Kind of coupled with 1, but learn Algorithms and Data Structures. If you never program than this isn't worth doing, but algorithms is math heavy and most companies that want to hire people to do algorithms expect a base knowledge, and basic knowledge of data structures is a MUST in that scenario)
4) Try applied classes! Other departments will not eat you! I promise... unless it's the department of cannibalism...
5) FINISH projects! Make sure whenever you get involved with a project that you push as hard as you can to get something finished and a "product" to show off.
6) Talk to professors outside of the department if they do something you think looks interesting. I don't mean to stress coding so much, but coding is something that everyone outside of CS departments (since coders are a dime a dozen there) needs, at least in the hard sciences and engineering.
7) For someone who doesn't plan on going into academia... internship >> summer classes. Search far and wide for these, they're extremely valuable and show that you can handle a work environment in addition to being able to handle an academic environment.
These are most relevant to undergrads, I haven't a clue what a grad student should do b/c I haven't gotten there yet!!