Zonealarm is insufficient. Zonealarm plus virus-scanner is insufficient. The Nimda worm used a flaw in Internet Explorer 5.0 (not 4.x, 5.5, or 6.0, just 5.0) in which if you connected to an infected webserver, your machine got infected through an Activescript setup that managed to circumvent IE's "built-in" protection against such stuff. Once this happened, you machine started scanning others to infect.
Since Zonealarm stops suspicious incoming connections, and a virus-scanner can only stop a virus it knows about, had that been your protection, you could have gotten infected.
Since Black Ice watches outgoing connections, you still would have gotten infected, but you would have gotten a message the first time the worm tried to scan out, letting you know that some unauthorized program was attempting to open outgoing connections.
Really, learning how to secure your machine is best, but given Microsoft's inability to deliver relatively secure and securable products, running Zonealarm plus Black Ice plus a virus-scanner is the best (if incredibly resource intensive) method to secure yourself. Or just accept the risks of being connected (which is my choice) and plan on the possibility of needing to format and reload at some point.
RagManX