What the Manufacturers Say
There isn't really a consensus among manufacturers on whether you should break in your headphones, or how. Steve Guttenberg at CNET notes that some manufacturers recommend it, while others "scoff" at the idea (heck, Monoprice even talks about it on some product pages). Guttenberg asked John Grado of Grado labs, who had this to say:
...he said, "All mechanical things need break-in." He did not recommend leaving headphones playing continuously for a few days to hasten the process. He recommends using new headphones as you normally would, and after 50 hours or so the sound will be all it can be.
In short? Don't stress about it. Of course, that doesn't help you pick a new pair of headphones if they're going to sound completely different in 50 hours. So, let's take a look at what the science says.
What the Science Says
There isn't a lot of experimentation in the realm of headphone break-in, so we're using the word "science" pretty loosely here. However, Tyll Herstens over at Inner Fidelity has done a few tests that provide some insight. He first took a new pair of AKG Quincy Jones Q701 headphones—notorious as a headphone that needs a lot of burn-in—and tested their frequency response over time (twice). He found some evidence for burn-in, but nothing 100% conclusive.
Later, he decided to test what he could actually hear using a small, single-blind experiment. With the help of a friend, he listened to two pairs of Q701s—one that had been used for 1000 hours and one fresh out of the box—to see if he could tell the difference (without knowing which headphone was on his head at any given time). He found that he could, in fact, hear the difference between the new pair and the "broken in" pair:
It's clear to me, having had the experience, that there is indeed an audible difference when breaking-in a pair of Q701 headphones. I've seen measured differences, and now experienced audible differences. While the measured differences are small, I believe the human perceptual system is exquisite and able to perceive, sometimes consciously and sometimes sub-consciously, subtle differences.
I think it's important to say that the K701 (and therefore the Q701) are notorious for their need of long break-in. The differences I heard, while evidently fairly obvious to me, were not large. I'm absolutely convinced that, while break-in effects do exist, most people's expressions of headphones "changing dramatically" as a result is mostly their head adjusting and getting used to the sound.
It's just one set of experiments from one person using one set of headphones, but it does provide a little bit of insight. Break-in may very well exist, and in his tests, it was an audible change, but it didn't turn his headphones into a completely different pair of cans.
In the end, we agree with Grado: just listen to your headphones normally. If they're going to break in, they will. We wouldn't recommend buying headphones you don't like with the expectation that they'll break in, though. If you really want to be on the safe side, just buy used headphones instead of new ones. They'll already have quite a few hours on them, and you might even save a bit of cash. Everybody wins!