Wired can’t find any evidence that “burn-in” actually changes the sound of speakers, headphones, and microphones, concluding:
Indeed, all of this variation gets at the real thing people are reacting to when they buy new head- and earphones: mental burn-in. If you’re used to dark-sounding headphones, neutral ones may sound bright at first until you get used to the new sound. That flexible calibration is how many of our senses work. Light seems brighter after darkness, sound rings louder after silence. Chances are, a lot of what people attribute to headphone burn-in is actually just their brains gradually becoming used to this new sound or new setting.
I think this is exactly right. I’ve never noticed any effects of burn-in on any of my audio equipment — excellent equipment sounds great on day one, and underwhelming equipment never becomes more… whelming over time.