For most people bass quality and quantity loom large when judging headphone performance. Bass supplies the music's weight and power, so bass-shy headphones can sound thin and tinny.
Sure, the same argument could be made about speakers, but their bass is perceived in very different ways than headphone bass. Speaker bass is literally visceral, your whole body feels it, and you hear it filling the room you are in. Subwoofer bass is even more visceral, and there's no headphone equivalent for that.
So while a decent set of headphones can play low-bass frequencies that are in subwoofer territory, headphone bass never sounds anything like subwoofer bass. I started thinking about all of this after I read Tyll Hertsens' review of the Monster Beats by Dr Dre Solo headphones ($199) on his new Web site Inner Fidelity. Hertsens didn't find the Beats lacking in bass, but he wasn't impressed by the quality of the overall sound. I haven't heard that Beats model, but I liked the Beats Pro.
In the review Hertsens referred to the bone conduction phenomenon that is in large part responsible for the way we perceive bass over speakers, and to a lesser degree over full-size, over-the-ear headphones.
For most headphone buyers, including lots of fussy audiophiles, elevated bass response is preferred. No wonder so few headphones are designed to be "flat" or measurably accurate in the bass; most buyers wouldn't like them! So careful listeners like Hertsens have settled on a subjective standard that is perceived as flat, even though it still has too much bass. Hertsens and I think Etymotic's ER-4PT in-ear headphones sound accurate; I would also include Ultimate Ears Reference Monitors, MEElectronics A151, and the full-size Sennheiser HD 650 headphones in the accurate group. My bass-heavy faves include the Jerry Harvey JH-16, Monster Turbine Pro Gold, and Thinksound ts02 in-ear headphones; the Denon AH5000 and Monster Beats Pro full-size phones are also very good, very bassy models. The models listed above range from $75 to well over $1,000.
For me, bass precision and definition are at least as important as bass quantity. Too much bass can add a thickness to the overall sound so that bass totally dominates the music. Of course, if that's what you prefer, go for it.
I'd also add that where you listen to headphones influences the perceived bass level. When you listen in a quiet room bass seems much louder than it does in a noisy environment. Trains, buses, cars, planes, and noisy city spaces all have a lot of low frequency noise and rumble, which masks the headphones' bass. Noise-canceling and noise-isolating models aren't effective at low frequencies, which are perceived through bone conduction and your whole body. So the more environmental noise there is, the more bass your headphones will need to supply to be heard. In other words, if you rarely listen in quiet places, going for a bass-heavy headphone might be a smart idea.