Something I was wondering about: Why is one still using transformers for vacuum tubes? I know that they need higher voltages than usual, but do they really need AC voltages? Or can't one simply use DC/DC converters to generate this high voltage? That would remove those ugly transformers, and just leave the tubes on the outside.
To complete Nils’ answer, in audio applications, transformers are needed to adapt the low speaker impedance (generally between 4 or 16 ohms) into a load suitable to power tubes (generally several kilo ohms). As the output power raise, the biggest transformers need to be. In the case of a single ended output stage, they must use class A mode. A constant current goes through the transformers and does saturate its core. They need to be air gapped hence over sized to provide a reasonable primary inductance while standing the constant current.
This is one big reason why an output watt is so much more expensive with tubes as compared to transistors. In hi-fi applications, the output transformer is responsible of the amplifier’s output bandwidth limitation (and phase twists) due to stray capacitances and leak induction. In the other hand, it provides a galvanic protection to the (maybe expensive) speaker system.
For a stereo amplifier, that makes at least 3 transformers (1 power supply, 2 output) that need not to induce noise into each other. As tubes use high voltage (up to several kV sometimes) self-inductances are often used in CLC cells to filter the 100Hz ripple out of the power diodes. They have values from several Henrys up to dozens of Henrys and are as big as a transformer adding a bit more weight to the whole.
That is why tube amplifiers are -- most of the time -- so heavy.
Remember that the anode voltage is only a part of the voltages you'll need to supply a typical tube circuit.
Along with the anode voltages you'll also need a beefy supply for the heaters (usually 6.3V, several amperes) and often a second high voltage for the screen grids.
If you're designing with DC/DC converters you can get the required voltages just fine, but in the end it's often cheaper to just get the right transformer made.
For musical applications (guitar amplifiers) the power transformer is also one of the sound defining elements. In guitar amplifiers the power transformer is often designed to run close to saturation. Reason for this is, that if you get a power surge (musician playing a note) the supply voltage temporarily drops. This lowers the output volume. Once the input signal fades away the voltage rises again and the output volume rises with it.
The end effect of this is, that you'll get a slight but natural sounding compression effect which lots of guitarists find very musical.