Depends.
If you display static content on it for an extended period of time like on a store unit or on-screen buttons, then it will burn-in. Not quite as quickly as some have stated, and certainly not as quickly now compared to older OLED panels, but it's still an issue. For instance, the Galaxy S6 edge store units I've seen have suffered from pretty bad burn-in after a year of service, as they're powered on for almost the entire day at maximum brightness without the screen going to sleep. That's an extremely high-wear situation and a phone won't go through that sort of usage pattern (screen on 24/7 at max brightness) in the hands of consumers, maybe even for its lifetime.
Which brings me to this. Consumer units will suffer much less drastically compared to store units. They'll last for years with normal usage, though exceptions such as some Nexus devices with OLED panels exist. In most cases, however, you should be fine. I still have a 4 year old Galaxy S3 with the original display and it hasn't burned-in yet. Very impressive.