Can I use the Unity launcher icon to minimize applications/windows?

For 14.04 & 14.10:

An unsupported capability was added to Unity for Trusty. Unsupported means that Canonical do not guarantee this capability moving forwards towards Unity 8.

However, from a LTS point-of-view this gives those users at least 5 years with just this capability. This is not directly available through the standard GUI.

For a safe way, reach for a terminal and copy & paste the following:

gsettings set org.compiz.unityshell:/org/compiz/profiles/unity/plugins/unityshell/ launcher-minimize-window true

To undo this change:

gsettings set org.compiz.unityshell:/org/compiz/profiles/unity/plugins/unityshell/ launcher-minimize-window false

For an unsafe method, you can use compizconfig-settings-manager :

1. Launch the application and click on Ubuntu Unity Plugin:

   

2. Switch to the Launcher tab and put the checkmark beside Minimize Single Window Applications (Unsupported) to enable this feature.

   

For 14.04:

See this answer.

For 13.10 and below:

Because Mark Shuttlewoth decided it, at least for now?:

no, clicking on the icon will not minimise the app. We have a minimise button for that, it's prominent.

At least, that bug now has the status opinion which means the developers won't fix it for now, but wait for community discussion.

So if you would like minimize on click too, make a clear statement at launchpad.