I point out this bass issue because some vendors design their headphones to emphasize bass "kick"—in part to stand out from other headphones in the store, and in part because some people really want that visceral impact. But such headphones often become fatiguing to listen to over time. If you're interested in accurate audio reproduction, be careful not to be wowed by emphasized bass. (The same goes for exaggerated treble detail.) The best approach is to audition a set of headphones for several hours—or, even better, several days—with a variety of music. If the headphones still sound great at the end, there's a good chance they'll satisfy you over the long run.
Headset functionality and inline control modules: Several years ago, thanks to the popularity of the iPhone, a number of companies started making headphones with a remote/microphone module on the cable, much like the inline remote on the iPhone's stock earbuds. At the minimum, the remote features a multi-function button for controlling media playback; making, taking, and ending phone calls; and taking advantage of iOS's Voice Control feature. Newer models include two additional buttons for adjusting volume. The module's microphone can be used to talk on the phone, make voice recordings, and give Voice Control commands.
Since the original iPhone's debut, Apple has standardized on the special headphone jack required to support these features. You can now use inline-remote headphones with every iPhone, as well as the iPad, the iPod touch, recent non-touch iPods, and recent Macs. This has led to even more headphone models with an inline remote/mic module. This is good news for Apple-owning headphone buyers, as it gives you many more products to choose from without having to give up the convenience of the remote and microphone.
Fit/comfort: Unlike most consumer-electronics devices, you actually wear headphones. So how well a set of headphones fits you—your head, your ears, and even your ear canals—plays a significant role in your long-term satisfaction (or lack thereof). I include a few comfort-related tips below, when describing the different types of headphones, but reading about a particular style is no substitute for actually giving a product a test drive (or a test run, as the case may be). If at all possible, try to find a local retailer that carries the model(s) you're considering, so you can actually audition the headphones on your own head and ears.