Question: Can I connect iPod to my home stereo? Answer: Yes. With its powerful 60 mW amplifier and 20 Hz to 20 kHz frequency response, iPod will sound great on your home stereo. Third-party stereo adapters are available for listening to your iPod music library using home stereo speakers. Compatible devices must be self-powered and support audio output through a 3.5 mm headphone jack. For optimal sound quality when using external speakers, set the iPod volume at less than half the maximum output and adjust your listening volume through your stereo controls. This prevents overamplification, which can cause distortion and reduce audio quality.
The most common headphone amp circuit is called the "C Moy". When you have a signal with zero DC bias you get the fun of making virtual earths and +/- power supplies.
You also get more problems, when you put it in a car - and try running everything off a single 12V battery.
"I also know that you are really not supposed to use a headphone output to drive an amplifier directly, because they tend to have different impedance characteristics."
Impedance differences are not the issue. A headphone output can certainly be used for driving an amplifier input, but - unlike a fixed-output-level line-level output - simply needs its output level to be set properly as headphone output capabilities will vary. In the case of an iPod/iPhone headphone out, there may not be much difference between its max voltage output and that of a standard line-level output.
Anyone who claims to be offering Audio and delivers it with a DC bias needs to be shot (or at least have a swiftly administered kick to the rear end). As Antedeluvian says, if you do have one you can use a capacitor to get rid of it. While Antedeuvian's suggestion of a ceramic cap is good, you could also use an electrolytic if you know which way it's biased (or you can get non-polarised electrolytics these days). though some purists do frown upon electrolytics for Audio, I've used them for years and had no real problems unless they go dry...which takes many years....
Most audio equipment has the standard 3.5 mm stereo jack output which implies a common ground. If this is the case then there cannot be a bridge output circuit, in which both speaker terminals are live and have a DC bias (if you had, say, a 10V supply, then both terminals would be at 5v in the absence of a signal. When you have a signal the terminals would move in opposite directions).
Bridge amps are commonly used in things like phones where you only have one speaker and you don't have to worry about common grounds. And in high-power audio amps - if you double the effective output swing with a bridge, you quadruple the power! And you can usually use seperate wires for each speaker - again you don't have to worry about common grounds.
I think most phones these days would use class D amps - basically using pulse width modulation - which has far higher efficiency. I found a couple of class D amps in a TV I pulled apart recently.