There are a lot of variables in headphone measurements that can make some of the specifications pretty meaningless.
When you put on headphones, an acoustic chamber is created, by the space in the headphone cup AND the airchamber that leads to your inner ear. It's a resonant chamber and since ears, like fingerprints, are different from person to person, it's a good bet that headphones will sound different from person to person. That means the frequency response will vary considerably.
You're also putting a small loudspeaker right next to your ear, so you don't need to turn it up very high to cause damage to your ear, but some high impedance phones, like the 600 Ohm AKG 240's require a lot more power to have the same loudness as a 32 Ohm set of phones. If the amplifier is marginal, it can cause clipping and distortion in the headphones, even though the phones aren't being pushed hard.
Most headphones only require a few hundred milliwatts of power (500 milliwatts = 1/2 watt), so they shouldn't tax your amplifier very much, especially if you have a headphone distribution system (like the Furman or the Rane).
Volume controls on headphones can create some serious problems for studios as well. Those volume controls are usually simple pots that go across the output of the amplifier and when they're turned down, you hafta crank the amp to compensate, which can burn out the pot or worse add distortion due to amp clipping.
As others have pointed out, the sound changes depending on the person listening, so you have to listen critically to determine which headphones are right for you. Open ear headphones usually provide the best frequency response, but offer no isolation. Closed headphones provide good isolation, but at the expense of comfort and often smooth response.
Open ear Grado headphones, for example, are wonderful sounding headphones to listen to music on, but they make everything sound good, and it's hard to use them for critical listening. The Sony 7506's are pretty much standards in the industry, but they have a high fatigue factor and hyped top end, which can kill your hearing after a long session.
If I've missed anything, lemme know and I'll try to answer it.