Ticking 'Notification light' under 'Settings -> Display' is the requisite for your LED to work at all. As soon as you disable this no app should be able to trigger the LED signal again.
I suppose that the notification itself is not handled by the system because it doesn't appear for every notification. It's more like every app can take advantage of it. I don't know every app which is capable of using the LED - just some of them; but they have already been mentioned in this thread. Some apps don't support the LED notification light, some do and even let you customize its color.
If you want an all-in-one solution to customize colours for different apps I can recommend "Light Flow". I bought the paid version and I'm totally satisfied. Just be sure that those two options are activated, else the app can't control the notification light.
-> Settings -> Security -> Notification access -> Light Flow activated
-> Settings -> Accessibility -> Light Flow -> On
I didn't like Facebook messenger to be green. I turned it blue. WhatsApp is green, SnapChat is yellow and so on... Works like a charm for me :3
#1: Samsung Omnia 7 _ sold on eBay.
#2: HTC HD2 _ sold to my brother.
#3: Samsung Galaxy S2 (GT-I9100) _ sold to a friend.
#4: LG Google Nexus 5 (Hammerhead) _ my current beast! <3
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".: ~' Das war erst der Anfang deines Endes! :.