itunes opens on its own

It's the Resume feature of Lion:

Managing Mac OS X Lion's application resume feature.

If you shutdown your computer you should get a dialog asking if you want applications to resume on the next startup. Simply uncheck the box to prevent that from occurring. Open General preferences and uncheck the option to Restore windows when quitting and re-opening apps. You can also install a third-party utility to control resume features on individual applications: RestoreMeNot or Application State Cleaner.

Does this happen randomly while the system is up and running, or just at start up? If it's just at start up you can stop it from opening by going into System Preferences, selecting Users and Groups, and then in your account click the Login Items button. Remove iTunes from the list.