First let me say that some headphones require a headphone amp or at minimum a home stereo receive amplifier to sound their best because of two reasons.
1.) The sensitivity on the headphones is low. This is the measure of how many volts / watts are needed to deliver a particular volume level. The higher the sensitivity typically given in dB the fewer volts / watts are needed to drive the headphone to adequate volume levels.
2.) The impedance of the headphone is rather high which changes the output power of the amp / device driving them. Different headphones amps will drive different impedance loads...well differently. The higher the impedance typically the less current is needed to drive the headphones. This is a little tricky because there is the needed power to move the drivers and then there is the power needed for the voice coils. In general the higher the impedance the less current is needed to drive the headphones or the less current is drawn from an amplifier. The general rule I use whether I need an amp with a particular headphone is the 80 Ohm rule. If the headphone has an impedance of 80 Ohms, but more than 20 Ohms, then an amp is generally not needed as long it the headphones also follow rule 1 above.
To better help you please list what headphones you are looking at. There are many of us who have had a ton of headphones over the years and perhaps one of us can prevent you from making an expensive choice that ends up making you unsatisfied. For example I shy away from headphones like the HD-650 and HD-800 because not only do they have high impedance, especially regarding AC, but they are really laid back sounding. This means that the sound appears to emanate through a thick pillow before it enters your ear. At fist you will think this is ok and perhaps after some magical burn-in the headphones will sound better. This is simply not true. Those two headphones will sound this way forever, save being driving by a balanced amplifier, and there is nothing that is going to change it. On the other hand headphones like the Denon AH-D2000 do not have this issue. The AH-D2000 has an impedance of 25 Ohms and are very easy to drive so no amp is needed. Better control of the current / voltage to the headphones will results is clearer and more controlled bass, but the headphones sound fine from a portable device.
Depending upon your budget and sound needs here are my recommendations for headphones. They are organized by build quality and sound quality. The increase in price is simply corollary.
1.) Creative Aurvana Live typically priced around $75
2.) Audio Technica ATH-M50 found around $125 and well worth it
3.) V-Moda M80/V80 priced right around $200. These are very portable and built extremely well. They are on-ear and not over the ear.
4.) Denon AH-D2000 priced around $310. These are one of my personal favorites and I use them at my desktop computer all of the time.
As for amps none of the above headphones need an amp, but the AH-D2000 will sound a bit better with one. I suggest the Total Bithead from Headphone.com to start. It is very reliable, well built, great sounding, little amp that also comes with a DAC built in. It can be driven via USB or by 3.5mm / 1/8 inch plug from say your portable device. It can be used as a portable amp because it is battery driven, but it can be USB powered without having batteries in it at all. No this device is not necessary, but it is an affordable way to improve on better headphones.
