FCC Part 15 is the US standard for non -intentional radiations from electronic equipment of all kinds, as well as intentional radiators used in certain services, such wireless local area networks, cordless phones etc. The levels specified there are such that a device meeting the requirements could radiate a signal on a frequency that caused interference - most probably, but not necessarily only, with DME or TCAS receivers.
There are corresponding European requirements. (These are 'EN' or 'European Norme': they are produced by ETSI, the European Telecommunications Standards Institute for comms type gear, and CENELEC - European electrotechnical standards committee for other gear) Incidentally, unless the device is CE marked, its use in the UK is illegal under the Electromagnetic Comaptability Regulations 1992, although in practice, that bit of the regulations is honoured more in the breach!
Most radio receivers are of the type known as 'superheterodynes' in which the incoming frequency is converted to another one for signal processing. This conversion uses an oscillator, which is the fundamental part of a transmitter, and there specific limits as to how much radiation is allowed and on what frequencies. Domestic equipment has quite lax limits, one reason being to allow TV detection! The EU Automotive Directive has got some real stupidities in that it allows considerably less radiation from a car radio than a fixed one, so that when driving down the street, you don't upset somebodies radio reception, but you can do it permanently. There are no special protection limits for any band used by aircraft, which considering that FM broadcast radios can radiate a lot of energy into the VOR channels, seems crazy to me.
It has been claimed that radiation from receivers was used by U boats to home on convoys in WW2, although I have my doubts on that one.
Aircraft aren't that good on immunity - there's been some discussion on the Passengers and SLF list abt this. There is, for example, a limitation on the use of Electronic News Gathering (ENG) equipment at and near airports because not all airliners can be guaranteed to have the necessary immunity to the field strengths that ENG can cause. Tornado fighters are renowned for their EMC difficulties, too. I'm inclined to think that there's a lot of 'say No because we don't know' involved though, when you consider that radar at LHR and the field strength that puts out at aircraft - when they're landing, too. There was a statement at a European meeting (from the CAA, if I remember) that they expect it will 2020 before immunity to 20volts/metre will be established in aircraft. Maritime safety radios require immunity to 10volts/ metre; cordless telephones and the like 3v/m and TV sets 1.8v/m. Portable radios have no requirements at all.
To put things in perspective, a typical mobile phone at full power will produce a field strength of about 0.4 volts/metre at 10 metres distance.