My system? I currently oversee a citywide network including government, schools, Utilities, and Libraries. Lots of Servers of many flavors and about 3500 desktops. This is my "retirement" job.
I've seen more than just a few invasions. There are many ways a virus can enter a system, even with a firewall in place. An example is that for schools and libraries to function, students and the public save their work on thumb drives they bring from home. They can bring trouble from home, and no firewall can prevent it. A good anti-virus can stop it, and prevent spreading it. It can also keep a log of what gets caught, so we know that viruses DO get into systems. Once one desktop is infected, it "can" spread to the other 3500 desktops on the same network. That's why we also run virus protection on servers. One desktop with a virus can bring a large piece of the network to it's knees by a flood of packets sucking up bandwidth.