Problems shutting down iTunes

are you just closing the window by clicking the red "X" button or choosing "Quit" from the iTunes menu or pressing "command-Q".

thats how Mac OS X works. every application that is document based i.e. can open more than one window does not quit when you close the window. this is useful if you want to keep the applications open for quick access (as its still in RAM) or for example if you want to keep iTunes playing.

there are also applications that are not document based and do quit when their window is closed like System Preferences, iPhoto, Disk Utility etc.