From a sound quality standpoint, let's start with the "potentially" worst situation and work our way up.
1) Bridging: Some stereo power amplifiers have a "bridging" option wherein, by the flip of a switch, the output of the two channels of the amp may be combined for increased power, at the expense of increased distortion. If you are in a pinch for more power in a channel and have a "bridgable" stereo amp handy, great. But that amp will generally have better distortion specs when operated normally. The audibility of the increase in distortion arising from operating in bridged mode is subjective, however.
2) Bi-wiring: Some two-way (or "more-way"!) speakers are thought to sound better if two sets of speaker wire are run from an amp's output to the two separate sets of inputs on speakers that are capable of bi-wire operation. In this arrangement, the (+) side of one end of the two speaker cables are twisted together and connected to the (+) side of a power amplifier's output and the (-) side of one side of the two speaker cables are twisted together and attached to the (-) side of the amp's output connector. At the "bi-wireable" speaker's terminal plate you will encounter "LF" (low-frequency) and "HF" (high-frequency) input terminal pairs. Here a (+) wire from each of the pair of speaker cables is attached to either a (+) LF post or a (+) HF post. Likewise, a (-) wire from each wire is attached in turn to a (-) LF and HF post on the speaker. The reason given for an improvement in sound is that back electromotive force, or "back EMF," energy generated by the voicecoils in the speaker reflect back into the speaker cable, potentially causing the high EMF from a woofer voicecoil causing interference to the operation of the tweeter, whose voicecoil has a very low back EMF and can easily be swamped by the back EMF from the woofer. In other words, the woofer, responding to an input signal, moves as it should, but in so doing creates an unwanted signal on its voicecoil which is then sent back through the speaker terminals and into the tweeter, interfering with the tweeter's operation. That a lower electrical impedance can ordinarily be found back at the amplifier's output terminals than will be found right at a common input point at the speaker itself is cited as the cause for the improvement in sound resulting from a reduction in back EMF interference from the woofer to the tweeter.
3) Bi-amping: Here, the woofer and tweeter not only get their own dedicated wire, they also get their own dedicated amplifier. This arrangement is thought to further improve the back EMF situation. This is a tenuous argument, however...one whose efficacy is dependent on the highly variably electrical environments which reside in the many different amplifier designs that are possible. Sometimes the assertion might be efficascious and sometimes not. One thing which is facilitated by bi-amping though, is the possibilty of resorting to an active crossover network, operating at line level ahead of the power amplifiers, allowing one to eliminate the passive high level crossover networks which are built into the speakers. Crossover networks are filters which are used to selectively send certain frequency bands of the signal to speaker drivers to prevent driver damage and/or distortion which might otherwise occur when feeding signals into a driver for which it is unsuitable to reproduce. Another benefit of utilizing an active crossover network ahead of the PAs is to improve the power output capacity of each PA by reducing the bandwidth of the signal that it is required to amplify.
I should add that there are commercial examples of speakers which can accomodate four- or five-way drive from seperate amps for each of four or five drivers. Some think that this is all Voodoo, and I can't personally cited any papers that confirm measurable performance improvemnt from bi-wiring or bi-amping, but there are plenty of speaker manufacturers who claim to have documented evidence that this is so and I can tell you that I have personally observed subjective improvements in sound from bi-wiring as well as both bi-amping and tri-amping some speakers that were designed to accomodate such operation.
I'll bet you're sorry that you even asked, now! And thanks for reminding me...I've had my all-Magnapan surround systems for about 1-1/2-years now and I haven't gotten around to bi-wiring it yet!
[This message has been edited by Dave McRoy (edited July 10, 2000).]