gnome-shell doesn't have a minimize button because it doesn't have an application list for the window to minimize to; minimized windows just disappear. You can only find them in the activities overview or the alt-tab list.
Also note that you can still minimize a window by right-clicking on the title bar and choosing "minimize"; you just don't have a button for it.
> ...minimized windows just disappear. You can only find them in the activities overview or the alt-tab list.
... which is actually really cool. They're still very easily accessible (a single mouse-flip or keyboard sequence away), but completely out of sight when I'm not using them.
The windows-style task-bar with 75 bazillion unreadable entries always seemed pretty annoying (and often unusable when any number of apps are open); Gnome 3 does things much more elegantly.
That's one of the things I really like about gnome 3 / gnome-shell: it mostly stays in the background out of my way, but is quickly available when I want it.
Also note that you can still minimize a window by right-clicking on the title bar and choosing "minimize"; you just don't have a button for it.