The headphone topic has been a popular one, and many times while reading it I've wanted to create a related topic to discuss headphone amplifiers.
I think in many cases, the audiophile community tells prospective enthusiasts that they have to spend huge amounts of money, or don't even bother. This probably leads many people to distrust the advice they receive. Well, in the case of headphone amplifiers, I hope people won't ignore the advice that headphone listening can be significantly enhanced with the use of a dedicated headphone amplifier, as well as the use of a decent DAC (digital audio converter) if you're listening to music output from a computer.
We can get into the discussion of some higher-end headphone amps, but for now I want to discuss the "entry level" headphone amplifiers, the kind that might be purchased by someone who is not completely convinced they will change the way a given set of headphones sound.
Lately, there are some good, high-output headphone amps for not too much money. My latest is the Aune T1, which is a USB DAC as well as an amp, and is really amazing quality for under $200.

Schiit (see
http://www.schiit.com ) makes some cheaper models which won't quite stack up to their Lyr or Mjolnir, but at least output sufficient power that even a high impedance headphone will perform pretty well. The new Magni model us just $99!
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Also if you have any DIY abilities, you can build one of your own. I have a kit for an O2 (Objective2) headphone amp which has been sitting on my shelf... haven't found the time to build it yet. You can buy them pre-built for not much more than the price of the kit (see
http://www.jdslabs.com/products/35/objective2-headphone-amplifier/ ) and the sound quality is supposed to be especially good for the money.
Kit version:

Assembled:

I'm certain some people will look down on the suggestion that headphone amps under $200 could be adequate, but my purpose is not to suggest these are all the amplifier a headphone listener would ever want. This is just to show a few ways it's possible to try outboard headphone amplification for $100-$200, and gain a noticeable improvement in sound quality. I think people are much more likely to try something if they can do it cheaply, with less risk. Personally, I think it's unlikely a serious headphone listener would try one of these amps and fail to agree the difference was a great improvement over using the headphone output of their computer or iPod or stereo receiver. Once the listener is convinced, maybe they will want to step up to a mid-level or high-level amplifier. There are certainly many of those to choose from.
In my own listening experience, you can get excellent sound quality from an amp in the $500-600 range, and unless you're using very exotic headphones indeed, you might not need (or notice improvement from) a headphone amp more expensive than that. I have yet to hear a headphone amp over $1000 that convinced me it was better, though there are plenty of high-end amps I've never heard. I do understand that many people listening to planar or electrostatic headphones especially emphasize the importance of the amplifier, even more than with normal high-impedence headphones.