High bass headphones

not only do you need headphones but you also need something to drive them. My computer at home runs a SoundBlaster ZxR while my work computer has a Sound BlasterX G5. Both are paired with a set of Shure 750DJ headphones that produce very good sound with lots of bass.

The impedance, in essence, indicates how much power it takes to drive the headphones. That's not technically what it means, but if you're new to reading those specs, that's what you can think of it as. For reasons that are well beyond the scope of your question, in general, higher impedance headphones don't care what you use to drive them as much as lower impedance headphones, in terms of sound quality. The higher impedance headphones will require you to set the volume higher to get the same loudness as lower impedance headphones.

The stated frequency range is mostly useless unless you're neck deep in this stuff. Those numbers vary wildly based on how the manufacturer defines them. Each manufacturer uses a different definition, and that makes the numbers practically useless for the purpose of comparing two pairs of headphones from different brands. As a general rule, ignore these numbers. If you still want to give them some context, know that the human ear can perceive sounds from about 30 Hz to 20 kHz. Sounds above 20 kHz cannot be perceived by humans at all, in any capacity. Sounds below 30 Hz can be perceived as vibration through the skin only. Skin can perceive frequencies from 0 Hz (constant force), to about 500 Hz. If you're old enough to understand this, the uppermost frequency that you can perceive is at most 16 kHz if you're male, and 18 kHz if you're female. If you go to concerts or spend time around loud things, it will be lower.

The THD value represents how much the headphones distort the sound you play through them. This number should be less than 0.3% in general. Again, each manufacturer uses a different method to determine this, so you can't directly compare headphones from different manufacturers. If the value is under 0.3%, you're usually alright, though. Under about 0.5%, there is some question as to whether or not a human can perceive any differences.

Contact pressure indicates how tightly the headphones grip your head. The specific value is a measurement of the total force. If one pair of headphones has larger pads, they can be more comfortable even if they have a greater contact pressure.

That may be a bit confusing.

High impedance headphones require less power at the same input voltage(this are easy on the amplifier) and are more quiet at the same voltage than lower impedance headphones. This actually means very high impedance sets require more voltage than many portable players(and some sound cards) can provide depending on the volume level you want.

For this reason you will have to ensure your sound card or device can drive your headphones. This is also the reason many users have headphone amplifiers.

Quick math.
Voltage / Resistance(in ohms) * Voltage(to get watts) * 1000(to get milliwatts)

0.5 volts @ 32 ohms is 7.8125mW
0.5 volts @ 150 ohms is 1.6mW
0.5 volts @ 300 ohms is 0.83mW

As you can see you may need more voltage to drive higher impedance headphones(how much will depend on your listening volume and how good the output amplifier on your sound card is).

Lower impedance is more common in low voltage devices(portable music players and phones tend to have a lower output voltage than PC sound cards.), most car speakers are 4ohm(lower for subs) because a car does not have the same voltage a house has(they have some other tricks as well).

While outside of the scope of this information. Higher output impedance(some line level outputs can have 100 or more ohm output impedance that has very little effect on other line level devices, but would suck for headphones) on your sound card could result in lower volume on lower impedance headphones as well. This is another story all together.

I 100% agree that an EQ is most likely what you are after for more bass.

I wasn't referring to power or voltage requirements at all with that statement. I was referring to electric damping of the transducer.

Basically, lower impedance headphones are easier to drive into resonance, and sources (i.e. headphone amps) have a harder time controlling the headphones. It takes a higher quality source (i.e. lower output impedance) to keep low impedance headphones under control.

Higher impedance headphones are easier to keep under control, and lower quality sources (higher output impedance) are able to prevent high impedance headphones from resonating.

In summary, a nice headphone amp makes more of a difference with cheap, low impedance headphones than it will with expensive, high impedance headphones. High impedance headphones will still generally perform better, regardless. It's just a wider gap with a cheap amp or a cell phone as the source.

I just want to make sure that waleeda does not go get 600 ohm headphones because they are easy to drive only to find out they do not have the required voltage(thus get almost no volume compared to a current pair of 32 ohm headphones.).

Lucky enough more and more sound cards are putting decent low impedance outputs or dedicated headphone sections on them. Some USB setups even have a charge pump to get more voltage than USB would allow to the output stage allowing more volume on high impedance headphones. My X-fi and Omni are WAY more than my 60 ohm(easy to drive on anything I have tested with) headphones could ever need.

FYI, neither the X-fi nor the Omni have low impedance outputs. The Omni is designed for high impedance headphones. When this is the case and they don't publish output impedance, you can safely bet that it's not a low output impedance. The X-fi is not designed for headphones at all. In general, that means both have outputs >=10 ohms. 60 ohm headphones continue to benefit down to 6 ohms of output impedance.

Most motherboards these days fall into the range of 16-200 ohms. There's still something to be gained from using an O2. The ODAC, on the other hand, isn't worth it anymore.

Back to the OP, the best option for headphones that you can rely on to sound good in all circumstances are the DT880s in 250 ohm, and the HD600s or HD650s in 300 ohm. These are the middle of the road options, not too soft, but still easy to drive. The DT880s in 600 ohm are the best sounding, but you won't have enough power to drive them at decent levels without a dedicated headphone amp.