That approach has the advantage of not normally taking up any screen real estate, but new users can easily forget what applications are running because a reminder isn't staring them in the face. Aqua's Dock is an attempt to improve on that precedent. The biggest advantage of the Dock is that it provides users with a place where minimized windows can go. Under the current Mac OS, minimized windows leave their title bar in place while hiding the rest of the window, which has always been an ugly behavior. In Aqua, windows reduce themselves to icons and put themselves out of the way.
Users can see what applications are running and manage windows a bit better.
Overall, I like the idea of the Dock. Unfortunately, it kind of falls apart in execution by trying to do too much at once. The bad Now, I fully expect that Aqua will be fine-tuned by the release of Mac OS X, fixing bits here and there. But some elements of the Dock need a complete overhaul. An icon can offer quick identification and information such as file type, but it should never be the sole source of information.