Anecdotally, my Moto X 2014 hasn't suffered anyburn-in, even on the taskbar or buttons, and I haven't heard other owners even commenting on it. Also, I haven't taken any measures to reduce it. I just love it for the near-zero brightness available through my Twilight/Flux app, no problems checking notifications in the dark!

From what I've read online the newer generation Samsung displays, those from say the last 1-2 years, have supposedly made big strides in dealing with "burn in". Apparently it's much less of an issue now, although still more common than LCD. Also, if I understand correctly, OLED doesn't actually suffer from "burn in" like LCD does, instead it's more "burn out" as the pixels, particularly the blue ones, degrade faster than other colors.

For what it's worth I have a Nexus 6P which uses a Samsung display and I haven't noticed any burn in yet, although I'm probably a very moderate user so that's not really saying much.

The Lumia 925 from 2013 had a gorgeous OLED display, and no burn-in or ghosting problems that I noticed for a couple of years.

They did take care of shifting the (beautiful, built-in) nightstand clock screen a bit around, I think.

(Adjustable color reproduction, you could go for "vivid" if you wanted, normal was fine.)

I had no idea the Lumia clock screen did that, it's a simple but brilliant solution to mitigate the problem. I'd love to see more work go into subtly shifting persistent UI elements around to avoid the issue. In particular I'd like to see the navigation keys and status bar on Android adopt something like that. I wonder if the UI elements would even need to shift locations or if it would be enough to shift colors so it isn't one particular color that degrades unevenly.

Not in my experience. Years ago I had one device that did get burn in, but it faded over a couple of weeks back to a perfectly normal screen.

You just said that you had a device that got burn in and yet at the same time you are saying that it's not a problem. Waiting couple weeks to get burn in disappear does not sound like a "no problem" thing

Yes, burn in is not a problem. I've owned many OLED devices, and the only one to get any kind of burn in used older technology. It happened when I changed the settings so the screen would stay on when plugged in. It was barely visible. It went away quickly. All this FUD about burn-in seems like just a boogeyman created by a ill-informed people, expecially in 2016.