Several things:
First, welcome to PF.
physxGuy said:
We're talking about high-wattage things like boilers, radiators, etc., things that use something like 500-1500W an hour...
I just said in another thread, this is like fingernails on a chalkboard to me. Its just watts. Not watts per hour. Watts is already a rate: Joules per second.
...but aren't as advanced as computer hardware (where you can tune everything in the BIOS). Can such equipment, even though it's rated for say 800W, consume more (810, 850, 900, 2000, etc. Watts) electricity? I don't know much about physics, but I think that they can't, because the resistors are protecting them from getting more voltage in, which is a part of the wattage equation.
Resistors don't protect these circuits nor do they provide any control. But they are so dumb, they do always run at the same wattage until they start burning out: If you always apply the same voltage to a resistor, you will always get the same wattage out.
For household devices, there aren't many that have potential to exceed their nameplate wattage, but some devices with motors can. Taking what people said about the vacuum cleaner and applying it elsewhere:
Your air conditioner's evaporator fan, the fan that circulates air throughout the house, was designed for a certain airflow and pressure. If you remove the ductwork and run it, you will decrease the pressure and increase the airflow. The net change will be an increase in power that may exceed the nameplate rating on the motor. This is a bigger problem on commercial systems, where fan motors have been known to burn out if they are tested before the ductwork is installed.
The condensing unit's compressor power use depends on the temperature of the air on both coils. I suppose the motor must be constant speed and the torque dependent on that temperature. If it is too hot in your house when you turn it on or too hot outside, or the condenser fan fails, the compressor power use will go way up, potentially exceeding the nameplate wattage.
For non-household HVAC systems, this is a bigger problem. Fans are driven by belts and pulleys and the motor spins at constant RPM or dies trying, so you can easily exceed the nameplate wattage on the motor just by changing the pulley. You can burn out the motor -- or blow up the fan, for that matter by spinning it too fast.
And even if the fan pulleys are sized correctly, if the motor has a variable speed drive, most can go as high as 120 Hz. Since nominal is 60 Hz, you can easily overdrive the fan. VFDs have safeties on them, but the ones designed to protect the motor (not the circuit) are manually set.