Hi sailormoonfreax,
Welcome to the Support Communities!
Are you closing the iTunes window, (clicking on the red dot), or are you actually quitting the application?
I would suggest force quitting the application, and then removing it from your Login items for your User account.
Another scenario that could be happening is a setting in Mountain Lion that reopens previously opened windows when you shut down or restart.
The articles below will explain these settings in more detail:
Mac OS X: How to quit an unresponsive application using Force Quit
http://support.apple.com/kb/HT3411
Mac Basics: Set your preferences
http://support.apple.com/kb/ht2490
System Preferences controls system-wide settings ("global" settings), and is available from the Applemenu at the upper-left corner of the screen.
Click the General setting and you can choose whether or not windows re-open.
Click the Users and Groups setting to adjust your login items.
OS X Mountain Lion: Set up login options
http://support.apple.com/kb/PH10650
I hope this information helps ....
Happy Holidays!
- Judy