Android: How to turn off annoying reminders from games and apps?

Do you ever get annoyed by those Android applications that keep reminding you?

"The Smurfs from your village miss you, come back and save us from Gargamel!"
- I actually had this one from a game called Smurf Village

"You have been absent from the game for too long, did you forget about us?"
- Random Android game

Etc.

I've been asked about this "problem" a lot in the past (mostly by the people at work), but I didn't know how to "fix" it so I just ignored them. "It's just a minor reminder, why all the fuss about it?" Well, that was until I had a sleepless night because of one such "minor reminder". The thing is - it's my wife who wakes me up every morning at 06:30. She does not use a sound alarm on her Android phone, but a simple vibration and the screen that lights up when alarm starts. She wakes up, turns off the alarm, wakes me up and that's it. Why do we do that? Because we have a baby sleeping in our room and he, just as all the babies seem to be doing, reacts to just about any sound or light that goes on for more than 5 seconds. ANY SOUND OR LIGHT. And if one of those reminders on her phone occurs, it turns on a flashing blue light that actually wakes the baby up. That happened a few nights ago and we had a rather sleepless night after that... Fun times.

So, if you want to turn off those things, for whatever reason, here's how to do it (screenshots are from my heavily modified Samsung Galaxy S3, so actual screens on your phone may look different):

Find SETTINGS on your application list

Go to Applications manager (or Apps, or Applications;
depends on your phone brand and/or Android version)

Select the application you no longer want to remind you of anything

Uncheck SHOW NOTIFICATIONS

Enjoy! Notifications for that applications will no longer annoy you. Unfortunately, I haven't found a way to do this for all apps, so you have to do it one by one. It shouldn't be much of a problem, there aren't all that many apps that do this anyway and the most famous one is probably Facebook app.