Hey, just got word from the Mathematics Research Group over at the National Security Agency (NSA: You know those guys, right?). The Director's Summer Program is a research-based 12 weeks in the summer where one works on issues involving pure mathematics, cryptology and communications technology. It is a paid position, prestigious, and of course highly competitive. It would also be a great career booster, even if you really have no intention of working at the NSA in the future.
The application process is all online, and the deadline is October 15. Give it a look.