A lot of misinformation in this thread. Looking at a store sample as a meaningful data point is just silly (or stupid). Those phones are on 24x7. No one actually uses their phone that way. I recently borrowed my son's Galaxy S3, which was used daily for more than two years. There's slight burn-in on the status bar, but since those icons are normally lit up anyway you don't notice it except under special circumstances.
^ This.
We have to understand that the units on display in the likes of Best Buy or the local carrier store are turned on 24/7, have their displays set to full-brightness and display the same thing over and over again on the entire display. That's an extremely high-wear situation, and one where a consumer-owned unit wouldn't normally encounter.
The wear-and-tear rate on those units is higher precisely because of that. That's why when some stores decide to sell these phones to clear their stock, they're really cheap as they've already experienced probably years' worth of normal consumer usage in just a few months.
The bottom line is this. Just use your phone normally and it will be fine.
And yes, OLED displays do have a higher tendency to "burn-in" compared to IPS displays. However, more recent OLED panels have become somewhat more resilient to that. It still occurs, but doesn't seem to be as bad as some of the early panels. I think this might be part of the reason why Samsung doesn't go with on-screen buttons on their phones. Though TBH, my S3 and even the old S2 don't have any noticeable trace of burn-in. The S2 probably might have some, but it's very hard to notice.
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