Windows – How to remove the Outlook 2010 icon from tray

From a similar question on SU.

PS Tray Factory may be of some use:

PS Tray Factory is a powerful and handy tool meant to flexibly control ALL the other icons in the system tray of the taskbar. PS Tray Factory will help you to manage all the applications that place their icons in the taskbar tray. When you have installed PS Tray Factory, you will forget about the problem of lack of space in the system tray, and will also get an easy, fast and handy tool to handle those applications. In short, ALL Windows users will get this handy and powerful tool at their disposal, whereas only Windows XP users have an idea of it. For the latter, we have made a nice surprise, as the features of PS Tray Factory exceed the standard built-in ones of this OS. With PS Tray Factory you can quickly hide system tray icons and easy manage them.

Assuming that when you say "...the system tray is minimized" you mean that you have "Hide inactive icons" turned on, I think you want:

(right-click Taskbar) -> Properties -> Customize (next to "Hide inactive icons")

Find the new mail icon (possibly in "Past Items") and change the behaviour to "Always Show".