None of the methods on this page worked for me - all of the suggested changes were already properly set. Turning them off and back on did precisely nothing too. But sometimes turning the settings back and forth won't take unless the confused device is restarted at a crucial part in the process, so here is what I did which finally fixed it for me:
1. Turn the notifications OFF in the app settings: (pull the notification area down > touch the gear icon to open Settings > More > Application Manager > All > Messaging > Show notifications (uncheck it)
2. Restart the phone
3. Send yourself the message and before it arrives, immediately exit the app by repeatedly hitting the "back" soft button (you need to do this fast – as soon as you hit Send). You should NOT receive the notification at this point.
4. Restart the phone
5. Send yourself another message and before it arrives, immediately exit the app again. You should still NOT receive the notification at this point, but by now you will have forced the phone to accept your own "notification off" setting (I love reverse psychology)
6. Restart the phone
7. Turn the notifications ON in the app settings: (notification area gear icon to open Settings > More > Application Manager > All > Messaging > Show notifications (check it)
8. Restart the phone again (I know, it's a pain in the keester, but it's all in the restarts)
9. Send yourself yet another message. Again, before it arrives, immediately exit the app. At this point I did receive the notification, but if you do not, restart the phone one last time and try texting yourself while doing the whole bailing-faster-than-a-hamster shimmy.
IMPORTANT: The native texting app won't notify you of incoming messages when you have the thread open (even with the notifications on – that's a default behavior as there is no point in notifying you about incoming messages while you're looking at them). That is why you need to exit the thread BEFORE the text arrives by hitting "back" (home button might not be enough to do the trick). So if you are still not receiving notifications, make sure it's not a simple case of staring at your own thread while receiving your own texts.