I know I'm out of line in this thread providing a REAL answer, but I guess I'll have to live with that
Right now I'm involved in a government program with my university to work on computer security for the government. I am learning quite a bit in this program, but to be honest, so far I've learned far more from two main sources. The first is real job experience. There is a lot you can't teach and wouldn't even think to try and learn if you hadn't experienced it first hand. I've done several IT internships and during that time, although it wasn't my primary job, I picked up a lot of knowledge of what security problems exist, and over time, how to fix them.
Secondly, I know quite a bit from experimenting on my own and just trying to learn all I can because, and this is the truth, this is a field where if you aren't interested, you aren't going to be very good at it. Actually that's true of most things, but with computer security you are trying to counter the "hackers" who have a very big interest in this topic, so you better care just as much about this stuff as they do.
Which brings me to another point. Networking knowledge is good, and it's absolutely necessary to know the OS you are trying to secure inside and out, but unless you want to develope your own security tools, programming is not really necessary. Computer security is more IT than engineering (movies to the contrary). I'm studying computer engineering as part of this security program, but it's not really necessary to be good at the security end of things. This whole Hollywood idea of some dude typing madly at a keyboard to break encryption on the defense network is not exactly the real life picture of security people. Security is about good planning, well thought out policies, and effective implementation. That stuff is more important than the low level technical knowledge.
Edit: After reading other posts, I feel I should put a qualifier on here that I am interested in more of the higher level planning and implementation than specific issues in security (ie, designing good TCP packet filtering software). I don't mean to say that programming isn't necessary, more like it isn't really necessary for what I want to do. But it will be nice to have if I ever do end up needing it I guess