Class A: The output transistors are always on. All of the output devices reproduce the whole output waveform. The efficiency is bad (<25%) since the outputs are always on
Class B: There is transistor for the positive part of the output waveform, and one for the negative ouput. This is more efficient since half of the output devices are off at any given time. The problem with Class B is that it takes 0.7 Volts to turn on a transistor so with very small inputs neither the positive or negative ouputs will turn on. Which brings us to

Class AB: Same as class B except the output transistrs are biased in such a way that for small inputs both the positive and negative ouputs are both on. However when there is a mismatch between the pos and neg ouputs there will be what is called crossover distortion. Some Class AB amps have more than others. At very small output levels (less than a couple watts) this type will operate like a class A. The efficency is around 60%.

Class D: This is completely different than the previous types. With class A and AB the outputs just amplify the input signal. With class D the input signal is sent to a Pulse Width Modulation chip. This PWM chip outputs asquare wave with pulse widths varying depending on the input voltage. The PWM square wave is sent to the output devices. This turns the outputs on and off with varying widths. This output is then sent through a filter made of capacitors and inductors that returns the audio signal. This filter is what determines how well the output resembles the input. When the PWM signal is high the outputs are fully on (no voltage across output), when the PWM signal is low the outputs are fully off(no current through ouput). Since power is voltage times current theorectically there is no power dissipated by the output devices. Most Class D amps are for sub frequencies only and have efficiencies above 75%. Class D can be used for full range audio frequencies but the PWM frequency has to be raised and the filter must be designed properly. I have heard that Infinity had porblems with RFI in their full range Class D's a couple years back.
In the cases above the amplifier will have a power supply with a rail voltage of say +/- 30 Volts. In some cases the power supply will have two voltages, say +/- 30 Volts and +/- 20 Volts. The amp will use the lower rail voltage for lower power operation, and use the upper rail for high power operation. This will increase efficiency since it is lowering the voltage across the output device, and thus lowering the power dissipated by the output device.
A twist on this type is the BASH circuitry used by Blade, The power supply is basically a Class D amp whose ouput is always a couple volts more than the output needed. The output devices are a conventional class AB configuration, but dissipate much less power since there is only a couple extra volts across them.
A new kid on the block is Class T, I haven't done much research but I think it is like a Class D with a variable PWM frequency. It should have great efficiency with much better SQ than conventional Class D amps. I think Techman has looked into these chips and can shed more light on the subject than me.
Sorry that this is so long, and if there are any questions or corrections let me know. Any spelling errors must be tolerated, that took me a long time and I don't want to spellcheck myself.

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Sometimes the majority only means that all the fools are on the same side.

Use your ears to judge components, NOT your wallet! K.I.S.S.

members.tripod.com/Audiophyle

Well, Phyle, you missed a couple, like G, S, etc...

ShadowStar

:-D

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Back at ya! Hey, I havn't seen any of those deisgns in Car audio, with the exception of the class G in the rockford 5 channel jobby. Feel free to contribute SS!

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Sometimes the majority only means that all the fools are on the same side.

Use your ears to judge components, NOT your wallet! K.I.S.S.

members.tripod.com/Audiophyle

ShadowStar
What is class S? I haven't heard of that one.
Also do you have any good resources on class G? I don't think I have read much about it.

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Sometimes the majority only means that all the fools are on the same side.

Use your ears to judge components, NOT your wallet! K.I.S.S.

members.tripod.com/Audiophyle

JD

Class G - I mentioned it earlier but this design has two or more voltage rails and the amp switches between them depending on output voltage levels. The amp uses the lowest possible rail for increased efficiency.

Class H - Similar to(same as?) the BASH circuitry I mentioned. The voltage rails are constantly varying, staying a couple volts above what the output devices need. Takes the Class G to another level further increasing efficiency.

Class S - Named S for switching, this class was a switching design with a lowpass filter to remove the switching carrier. Over time this became the class D amp.

JD