Actually few tube amps are Class A. Most Class A amps are transistor.
Amplifier class is a complex subject, but basically if the tube/transistor conducts through 360 degrees (the complete cycle) of the waveform it is running class A. If it conducts for 180 degrees (half a cycle) then it is operating in class B. If it conducts less than 180 degrees it is running class C.
Class C is never used in audio applications and is only found in radio transmitters. It is very efficient, though.
Class A is very inefficient because the device conducts current equal to full power even when no signal is present. All this current becomes heat. Thus class A amps tend to be large, heavy, and expensive relative to their power outputs.
For audio applications, any tube or transistor operating by itself as an amplier stage must operate class A to ensure that the entire waveform is amplified. This is called single ended operation.
Some audiophiles think that single-ended triode power amps are the holy grail of hifi.
It's also possible to use two tubes or transistors in tandem to form an amplification stage. If the two devices are driven 180 degrees out-of-phase and their outputs combined to form the signal we have a push-pull stage. One nice thing is that odd-order harmonic distortion tends to cancel out.
A push-pull stage can run class A. This is still very inefficient since both devices conduct throughout 360 degrees of the waveform. In principle we could run them class B. Since a class B stage conducts for half a cycle, each device is effectively off for 180 degrees of the waveform. This produces a much more efficient amplifier.
The trouble with pure class B push-pull is that it's hard to get one device to start conducting and the other to stop without generating a notch (distortion) in the waveform. So we can fudge it - suppose we let one device conduct a little more than 180 degerees of the cycle - not so much that we're in class A but enough for some overlap between the devices. This is class AB operation (there are several subdivisions such as AB1 abd AB2 that depend on how much overlap there is).
Class AB amps are also very efficient and can sound quite good. As push-pull amps they can still suffer from crossover distortion if the circuit is not carefully designed and built.
Class A amps have a reputation for being very musical and warm (in more ways than one!) - but at a cost.
A designer can always parallel devices (tubes or transistors) to get more power. A single ended stage thus could have several amplification devices in parallel. Similarly, a push-pull stage could have several devices (same number!) in parallel for each leg of the circuit, A push-pull stage always has an even number of devices.
Think of class AB stages as being between class A and Class B. A class AB stage will operate Class A until a certain power level is reached. The level depends on how deeply in the class A direction the circuit operates. It can be anywherer from a fraction of a watt to hundreds of watts.
There are other amplification topologies such as class D (switching), but we'll leave them to another thread.