For most people, computer "security" is an illusion. Often corporations have tight firewalls, the "latest and greatest" filtering solutions, and they still have problems. That's because there are people involved.
I work in higher education, and some of the things we have seen are enough to make you cry. No matter how good your IT department is, there will be an administrative assitant or a professor somewhere that will write down their username and password on a sticky note (or use a magic marker and write it on the side of their monitor - don't laugh, it happened last semester) and negate all your security precautions. Or they will use their birthday as their password.
Your question was very broad, as there have been enormous volumes of information produced to address "computer security", but frankly the greatest problem we are facing right now are the newly ubiquitous USB pen drives. Pop it in, download large amounts of data, walk out, crack it at home. Sneaker-net is impossible to build a firewall or DMZ for.
Just my 2¢