Depends on the circuit, and what is the worst-case voltage that could ever be present.
Except for short-circuits, the worst-case should be the maximum voltage which could ever be present in the feedback loop. At an extreme, that's the voltage present at the speaker terminals (though it should be less due to the voltage divider used in the feedback loop).
The highest speaker voltage in an amp with a given power will occur at the highest impedance tap, usually 16Ω. Let's say the amp is 100w.
Power = Voltage2/Resistance -> 100w*16Ω = Voltage2
Voltage = 40v RMS
So a 100v cap will be plenty in this case. Smaller output powers will have correspondingly lower voltages present.
However, folks often already have the needed cap value on hand at 400v (or 630v) and use that. Manufacturers may use a 400v part because they're already buying hundreds of thousands of that part for other positions in the amp (or other products) and have an economic incentive to use a part not absolutely needed.
Last possibility is some folks may desire to have a part that will never fail. If the amp's B+ is under 400v (even at turn-on), then now matter how a short circuit is formed inside the chassis, or from any point within the amp, then the 400v cap will prevent a big fault current. However, it could make it harder to find the odd short circuit because of fewer destructive clues.
Be careful thinking massive over-rating will produce a more reliable amp. There's generally a cost, size and weight penalty for pursuing this approach, and a well-built non-overrated amp will likely live just as long for cheaper. Besides, as soon as you build something that's idiot-proof, someone will come along and build a bigger idiot.