possibly related discussion ?
https://bugzilla.gnome.org/show_bug.cgi?id=571109

Also sort of related to bug 607338.  But the question "do we need a special tiny button in the titlebar of every window to minimize it?" is a very good one.  Perhaps hotkeys and an item in the app menu is enough?  Perhaps they are too tiny and fiddley and accidentally triggered on touch devices?

I'm leaning towards removing both minimize and maximize.  Maximize can be done as a gesture (bug 630548).

I guess this could be accomplished using the button_layout mutter setting.  However, when I did that the theme didn't seem to recognize that it didn't have them there and drew the wrong close button.  Jakub recommended the following:
diff --git a/themes/Adwaita/metacity-1/metacity-theme-3.xml b/themes/Adwaita/met
index 50fc5bf..e81d5cc 100644
--- a/themes/Adwaita/metacity-1/metacity-theme-3.xml
+++ b/themes/Adwaita/metacity-1/metacity-theme-3.xml
@@ -960,7 +960,7 @@
 
   <!-- window types -->
 
-  <window type="normal" style_set="normal"/>
+  <window type="normal" style_set="utility"/>

I really like the idea described here : https://bugzilla.gnome.org/show_bug.cgi?id=607338
The "minimize" action is replaced by a "parking lot" action.
By minimizing the window, it goes to a reserved space in the overview (see http://d.imagehost.org/0672/minimize2.png)

I really like the idea, because eventhough you can mimic this behavior (parking application in reserved spaces) by using several workspaces (and DND), it seems that the developers tend to consider that different workspaces will be used by power users only (see http://jimmac.musichall.cz/log/?p=1126 and http://jimmac.musichall.cz/log/?p=1107).

So, I am only guessing, that removing the minimized button will make things harder to understand for regular users.
But in the other hand keeping the minimized button with the current behavior is even more confusing (where is this window ? I just minimized it ...)

IMHO, removing the button violates the Principle of Least Astonishment (http://live.gnome.org/GnomeShell/Design) and for me the "parking" behavior will be great to teach the beginners to use the different sections of the overview and workspaces. (Design a self-teaching interface for beginners http://live.gnome.org/GnomeShell/Design).

The situation at the moment: 
Click on "Minimize-button"  ->  hide this window

Note that depending on the use-case this can be very useful, since using by using the "Minimize-button", the window is out of the way - but the state/contents of the window is preserved. 

Removing these buttons is hardly a solution for most of the users. The vast majority of Users I know never use gestures - they do not even know that gestures exist. 

I think that there are different issues here: 
a) The minimize-metaphor does not correspond to the actual behaviour

Possible solution for a): Either change the metaphor from "Minimize-button" to "Hide-button" OR  Adapt the behaviour to the metaphor. The comments above illustrate how the minimize metaphor could be translated to the Gnome-Shell i.e. show a small "picture" of the window.

b) The ICON on the button do not fit to the Gnome-Shell. Typically the minimize icon is represented by a small bar. This fits graphically to the Window List in the old Gnome-Panel which is not used in the Gnome-Shell. 

Possible solution for b): Adapt the icon to the Gnome-Shell. If it is used as a "Hide-button" this should be visualised (e.g. by a single dot). It the button is used as a "Minimize-Button" than a small rectangle would be a more adequate graphical metaphor than a small bar.

At this point I think this can be done by changing the gconf key 
/desktop/gnome/shell/windows/button_layout = ":close"

Schema changed to :close, see

 http://mail.gnome.org/archives/gnome-shell-list/2011-February/msg00192.html

for detailed discussion. Sorry about the line wrapping, evolution wasn't
working so I used an incompetent web-mail substitute.