I've had a SGS Fascinate since the day they shipped on VZW - my phones haven't been afflicted by burn in, but possibly because I often change screens, and always use auto-rotate and use landscape mode often, even if it's in the dock, it uses the ICS alarm clock with a moving time.
However - I know it can happen. I received as an insurance replacement a refurbished unit that had the Samsung dock image burned into the display - it was like pulling teeth to get Asurion to understand what I meant.
So it seems it's all about how you use it. If you're one to leave the screen on high brightness and left on all day, you may want to reconsider those habits. But for those complaining why not use a SLCD.... once you spend time with the infinite contrast & deep blacks that AMOLED can give you, it's hard to go back to an LCD display.