It seems that to sell a GSM mobile phone, companies like Apple, Motorola, Sony Ericsson and many others invest a considerable amount of money in EMI testing them. Yet they still interfere with my stereo, radio, computer speakers, and other devices. Why?
The interference caused by GSM phones is an intentional radiator that is within the required limits of regulations.
I tend to blame the other devices for not shielding well enough. Any wireless device is going to have harmonics, its just a way of life and it just so happens that one of the harmonics with many GSM devices is in an audible range.
Take a close look at a typical FCC declaration of conformity:
"This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions:
(1) This device may not cause harmful interference, and
(2) This device must accept any interference received, including interference that may cause undesired operation."
The key word is harmful. Distortion or buzzing on speakers is not considered harmful. Annoying, yes, but not harmful.
Consumer goods like radios, stereos, etc. are built down to a price and typically have very poor immunity to out of band signals from devices like mobile phones. You could modify your equipment with filters, better quality mixers, and so on, but it will be expensive and a lot of work. Military equipment has to operate in close proximity to high-power signals, and a lot of attention is paid to screening and filtering, as well as circuit design, to avoid such problems, which is one reason why it is so expensive.
At least in Europe, although the EMC directive does not have a frequency limit, and the specifications often start by saying they cover d.c. to 400 GHz, in practice limits were only given up to 1 GHz.
I believe this was because it was deemed unlikely that any device would efficiently emit much unintentionally beyond this frequency, but that was all written before 2.4 GHz became so widely used (Wifi, Bluetooth, Zigbee etc). Therefore the audio kit wasn't tested for immunity beyond 1 GHz. In any case, it is usual to accept temporary deviations in analogue equipment, or any equipment, which self corrects with no intervention from the user. Otherwise you have the problem, in analogue equipment of deciding what level of noise is acceptable during an interference event.
It's worthwhile to note that a lot of audio equipment assumes that signals going into it will consist of audio frequencies, and thus that they do not have to worry about higher-frequency signals. Unfortunately, if the signals going into an amplifier cause distortion at any stage of the process, such distortion can generate unwanted frequencies from any combination of the input frequencies that happen to be present. Something like a crystal radio set can exploit this phenomenon; a 900Khz AM carrier modulated at e.g. 1000Hz will have frequency components at 900.5Khz, 900Khz, and 899.5Khz. Putting the signal through a diode will distort it in such a way as to generate 0Hz (DC), 500Hz, and 1KHz components (though hopefully the two sources of 500Hz components will cancel). The 1Khz component may then be used to drive an earpiece.
Unfortunately, it's easy for an amplifier input and output stages to exhibit such distortion effects in response to high-frequency signals. It is curious that such signals can become clearly audible even when they're just crudely coupled to relatively low-impedance audio cables, but it's worth noting that it's possible for the distance between a cell phone and an audio system to be a tiny fraction of its distance to the tower; consequently, a nearby audio device may pick up a signal that's a million times as strong as the one picked up by the tower.
The other answers here are mainly on track, but one aspect they haven't mentioned is proximity. When I hear interference from a GSM device, it's usually when someone is standing within 2-3 feet of a land-line telephone or telephone-related device (my home answering machine and the conference phones at my office are the main victims I've noticed).
However, the radiated emission limits (both FCC and CE) are based on limiting the emissions from the radiator at a distance of 10 m or more. This means the regulations are not designed so much to ensure that two devices sitting right next to each other won't interfere, but to sure that your phone doesn't interfere with a device in the next room, or in your neighbor's house.
In part, the specification at 10 m distance is simply meant to ensure a uniform test condition, because it gives a reasonable distance for "near-field" radiation effects to have fallen off and ensure the measured radiation pattern will be consistent with the interference effects at any distance in the far field.
But also, the regulations were developed in consultation with electronics manufacturers and they would have considered that trying to reduce radiation to a level where they won't interfere with each other at 0-1 m distance would increase costs (as alluded to in Leon's answer) to a point that would make many consumer electronic products unsaleable.