You should look at this API training about activity life cycle:
http://developer.android.com/training/basics/activity-lifecycle/index.html
and also this:
http://developer.android.com/training/basics/activity-lifecycle/recreating.html
As you can see, your activity can be gone because the user actively destroy it (using the back button) or the system can destroy it. If they system destroy it you can use onSaveInstanceState to save the data and onCreate to retrieve it. In that case you do not have to use SharedPreferences - just use Bundle as described in the link.
However, if you want to persist your data when the user close it, you should save your data when the call back onDestroy() is called. And retrieve the data when onCreate() is called. onDestroy() is called before the system thinks that your activity is not needed anymore, like when the user click the "back" button. In that case you do have to use one of the storage method provided by android, including Shared preferences. Like someone else said, it requires a "key, value" mechanism, so it might not match 100% with what you do. Using sqlLite is a bit heavy weight for this task, since your data is not really of a table type either (a single column table, actually, which is still not database worthy IMO). I think the best way to store your list is to use internal file. When onDestroy() is called, grab all your data and save to a file. When onCreate() is called, read the file and repopulate your list. You can read about android file system, including internal files here:
http://developer.android.com/training/basics/data-storage/files.html
As a close note, if the user press the "Home" button, your activity will not be destroyed. If he then "Force close" your app then nothing will be saved. If you still want to save it even in that case, I suggest you to save your data when "onStop()" is called and reset your list when onStart() is called.