Now that USB is mature and well established, many manufacturers are incorporating USB connectors into their instruments to allow the piping of digital audio directly to and from a host computer for recording. Even guitar effects from the likes of Boss and Line 6 now come with this convenient facility.
USB cables and leads are subject to tight production specifications. Just ensure that a USB 2.0 compatible lead is always used, as this is designed to carry the much higher bandwidth of the newer high speed USB protocol. Be aware that the maximum permitted USB lead length is 5 metres.
FireWire can also be used to transfer audio data, and like USB, the cable and lead specifications are tightly controlled, so you needn't worry about the make from the perspective of the quality of the signal transmitted, although there are some particularly rugged models available which are appropriate if you frequently plug and unplug. FireWire differs from USB in that it uses a peer-to-peer topology, which is another way of saying that no one - node - is significantly more important than another. In other words, audio devices can communicate directly with one another without the intervention of a computer.
In addition to stereo digital interface formats, there are several multichannel formats. With the Alesis ADAT multitrack recorder came the 8-channel ADAT lightpipe protocol for digital audio interchange. This technology is an example of a multiplexed signal transfer - signals for multiple channels of audio can be sent on a single wire (optical in this case), as long as the transmitting and receiving devices can encode and decode the information. USB, FireWire and fibre optics are all used for transferring multiple audio steams simultaneously.
Although originally designed for transmitting 8 channels of audio at up to 48kHz sample rates, the SMUX variation of the protocol allows ADAT connections to provide 4 channels of 96kHz, or 2 channels of 192kHz.
For stereo/dual channel transmission, S/PDIF and Toslink both work well. In electrically noisy environments though, Toslink may well turn out to be the better choice as it is interference immune, and does not suffer from potentially disastrous ground loops. AES/EBU is usually only found on high-end products as it is much more expensive to implement. It does however offer better signal integrity due to the higher voltage levels used, and by virtue of its balanced inputs and outputs.
MIDI leads are usually made from 2-core cable with a lapped screen, terminated at both ends with a 5-pin DIN plug. Only 3 of the 5 pins are used in each plug, but it was chosen for its high friction contact and low price. Although these leads are subject to less stringent manufacturing specifications than USB or FireWire, most standard cable lengths will have no problem transfering data without corruption. MIDI delays and timing errors are never caused by MIDI leads, despite what some may say. However, to avoid possible data corruption, the cable length should be no more than 15 metres. MIDI cables are designed to transfer performance and control information at 31.25kHz - audio cables should never be substituted.
These days many electronic musical devices use network cables and others inherited from the telecoms industry for control purposes. For example, the popular Line 6 Pod uses an RJ-45 (modem connector) and CAT-5 cable to allow it to communicate with a foot controller.
Bear in mind however, that just because a network cable is employed, it doesn't mean that the connected products have IP addresses (some do) and can automatically talk to each other - it may just be a convenient cabling strategy.