I might as well add my $0.02 worth here too.
This is a well known and allowed for condition in safety standards. It is referred to as "touch current" and was previosuly referred to as leakage current. The safe limit for touch current in Class 2 devices is 0.25 mA and this lies within the perception range for some people. Touch current is likely due to the current passing through small value capacitors connected between the chassis and the primary power circuits. This is usually for ESD (electro-static discharge) compatibility in the case of audio/video equipment.
There is no rule in the safety or wiring standards that prevents you from doing so, but introducing an earth is not a good idea since it may cause unintended earth loop currents to flow through other circuits. This can lead to humm and noise, etc.
Among other reasons, it also has to do with cost, but not as you might imagine. By floating the chassis there is no need to use audio baluns or isolating transformers in the input and output interconnection stages to remove extraneous circulating supply currents or to provide electrical safety.
I read some of the other replies and would also like to add the following.
- There is no prohibition on interconection of Class 1 and Class 2 equipment. The only safety related condition is that any earthing required for safety of the Class 1 device is maintained at the desired level. Which is 1.6 times the rated current of an inherent protective device (eg. internal fusing).
- Equipment that was marked "Do Not Earth" was often done so because the internal circuitry was "live" and separated from accessible conductive parts by double/reinforced insulation. Earthing the internal circuitry would be potentially hazardous in this case.
More commonly the "do not earth" instruction is for when the equipment is supplied to countries that do not have the MEN (TNC-S) mains supply wiring scheme. In those countries there is a separate earthing terminal or bonding point on the equipment chassis, and more often than not, no mains plug is supplied on the cord. Equipment that is to be earthed has a plug added, and the chassis bonded to earth at the time of installation. For floating chassis devices the do not earth instruction is to specifically draw attention to not to bond to earth.
- For small A/V and ITE, making Class 2 equipment costs almost the same as Class 1 equipment. Class 1 is of benefit in high power appliances like toasters, ovens, etc.
- Class 2 construction does not mean double insulation. Double insulation may be a type of Class 2 construction but reinforced insulation is now more common.
- Someone mentioned triple insulated wire is not common. It is now very common, being the preferred method to construct very small footprint concentric wound transformers in smal SMPSUs. The majority of mobile phone power supplies I have examined (say, since 2000) use triple insulated wire as the secondary winding. This way the static screen and the primary can be conductively coupled, doing away with the additional layers of insulation that would otherwise be needed.
Most of the above can be found in AS/NZS 60065 and/or AS/NZS 60950-1