I've been using Linux for four years, all that time the thought has been at the back of my mind that the bottom panel gets a bit full when I have multiple open windows. Something made me remember today that Windows used to group open windows when the taskbar was getting full. I quick Google search and I found that this is also possible in Gnome, although it's not the default. It's even possible to specify that windows are always grouped.
Simply right-click the little vertical "grip" bar to the left of the window list, and select preferences, as described here.