If you're binding your ListBox to say a BindingList, you can use the BindingLists's ListChanged event. The ListChangedEventArgs has an argument ListChangedType which tells you if an item was added, removed, moved or changed.
You can do similar things with similar collections.
If you're adding or removing items yourself, you can obviously directly tell some other piece of code to execute or you can just create and raise an event yourself, provided you have a ListAdded event:
ListAdded(this, new ListAddedEventArgs() { List = myList, Item = myItem });