As systems get more connected, and are being made more accessible through various networks, the need for security becomes ever larger.
Make sure that you learn about technologies, not just about particular APIs, or implementations for a particular language. Those are going to chnage in the future, while the underlying principles remain valid for much longer periods.
The
Security FAQ links to a number of resources that help understand the problems and solutions. I recommend in particular the interview with Bruce Schneier and the comp.risks newsgroup.