Do you use a Subwoofer when listening to stereo?

That is a reasonable explanation Tim until you get to the radiation pattern of line sources. Line sources project power (volume) better than point sources. To quality as a line source the speaker either has to be taller than the longest wavelength it is to reproduce or end at two boundaries like the floor and ceiling. People think of ESL being rather polite but if you make one 8 feet tall and put it in an 8 foot room the gloves come right off. The problem for subwoofers is that if you put a point source subwoofer system under a line source speaker it will disappear as you move away from the speaker. Now, if drivers are closer together then 1/2 the shortest wavelength they are to reproduce than they will function acoustically as one driver. This is the principle behind the  D'Appolito array. Four subwoofers running as high as 125 Hz this means they have to be no further than 4 feet apart. But to do 20 Hz the array would have to be longer than 52 feet. Fortunately rooms have walls and we can use them as boundaries so as long as your subwoofer array stretches from wall to wall you are in business. Thus my subwoofer system is functioning as one large linear array subwoofer producing one large wavefront. Remember line sources do not radiate up or down. If you but the subs against the front wall there is no early reflection point off that wall so only the floor and ceiling are comb filtering. On top of this you get all the benefits of a swarm system. Moving to the swarm as is normally used with say an 80 Hz crossover, to function as one driver the the subs would have to be within 8 feet of each other which is actually doable in most rooms. If you kept them all within 8 feet from one to the next what would happen? Tim, why don't you do that experiment and let us know what happens. I have no idea. 

drlisz, the type of music has nothing to do with this unless you only listen to string quartets. A good system will play anything equally well. If it can't it is not a good system.

Atmasphere, I am going to disagree on this one. My experience is different but I think I might go about it differently than most. Up at the crossover point I am just listening and I do not want to hear it. The subwoofers should just disappear(remember I use a crossover point of 125 Hz). It has to sound like I am listening to one speaker. As I evaluate lower down I go from listening to feeling. Do I feel that kick drum the way I do at the club. Are those low synthesizer notes shaking me the way they should. Does the room move under low organ pedal. Hearing is one thing feeling is another. Part of the thrill of live music are the visceral sensations you get.
These sensations are missing or greatly attenuated in most home systems. I started playing around with subwoofers in 1978 for this very reason. I wanted to feel as if I were at a live performance. Again, I can now move a subwoofer 15 feet just by delaying it 15 msec. I can change crossover points and slopes on the fly at one Hz increments 2nd to 10th order. You can hear these changes immediately. It is easy to demonstrate that with everything aligned perfectly those visceral sensations come through in spades any movement away causes instant deterioration in those sensations up to completely obliterating them.
Dukes instructions represent a reasonable way to set up his system without expensive test equipment. You can purchase his system for a very reasonable price commensurate with what most of us have to spend on a system. Brilliant. Using modern resources you can however go beyond this. You just have to be willing to put in the time and money.  

Atmasphere, phase is only half the issue time is the other one. I find it rather comical that people can say phase is not an issue. Wire one of your speakers 180 degrees out of phase and what happens to the bass. Any fundamental from impulsive bass sounds such as bass drums disappears. Most people would not notice this because their systems do not produce these fundamentals in the first place and I think this is what most of the mythology stems from.
Now it is true that the wavelengths are very long and physically getting a subwoofer 180 degrees out of phase would mean backing it up 15 feet and the degree of out of phaseness depends on the frequency. But, if you do that you have now created a 15 msec delay between arrival times making the situation even worse. Accurate bass transients at the listening position at least, requires the arrival times of the sound from each speaker to be exactly the same with the signal being in phase. In order to do this you need to be able to measure what is going on and then make the appropriate adjustments. In my case the computer makes the adjustments for me. I also have the ability to manually change delays and phase so I can demonstrate to you exactly what happens to bass transients. These are not something that you just hear by the way. They are something that you also feel. Now, I use four subwoofers but they are arranged in a specific way for a reason. They produce a single wave front without interference from the side walls floor or ceiling. There is essentially no back wall because of the way I designed the room. That wave front gets to my recliner at exactly the same time and in perfect phase at all frequencies as that of the satellites or main speakers. 
Swarm systems where you are placing the subwoofers at various random points in the room is a way of dealing with your typical room acoustics.
It is not necessarily the best way to integrate subwoofers with your main loudspeakers. Whether or not you can actually make it work satisfactorily? I have no idea. I have not measured a system set up that way. 

Nobil100, it is not just what you hear, it is what you feel. Eventually you will get a proper crossover and learn. Unfortunately, accurate bass below 40 Hz is a rarity is home systems. In order to use subwoofers at the state of the art you need digital bass management. Without it you are lost. If you think you can get it right just by listening...just keep listening. Listen to live performances in smaller venues like jazz clubs. See an artist like Dave Holland then buy one of his records. Are you even close?

 Adding subwoofers under the main speakers is just a cheap easy way to do it. The manufacturers would not be able to sell subwoofers otherwise. The Swarm system is a great way to deal with room acoustics which do cause a large share of the problems related to bass reproduction but not all of them.  

Thanx cleeds, you are right about the outputs.

Nobil100, no it is not fine to run satellites full range while adding subs for three reasons. First is you miss the opportunity to lower distortion and increase head room significantly in the satellites. Second is you make integration much more difficult. You are down where the wavelengths are over 10 feet up to 30 feet. Unless you are using digital bass management matching phase and time are difficult, usually by trial and error  moving the speakers and perhaps by using a phase control on the sub. Without a two way crossover there will be more overlap making the problem worse.
Digital crossovers can use slopes as high as 10th order which is actually too steep! Third is you will get a hump where the speakers overlap. Unless you can EQ the subs, keeping the system from booming at the overlap will force the volume down below the overlap keeping you from getting the power you need below 40 Hz. 
The hallmark of a good subwoofer system is that at a modest volume there is no difference in sound on subwoofer bypass until a really low note comes along. Use an acoustic bass solo and switch back and forth.
At higher volumes the decrease in distortion in the satellites may tip you off. 

No dbphd it is not!! You are likely to mono your entire system. You would have to take those outputs to another line stage then Mono that.

I wish to reiterate that just adding a subwoofer to a system without using a high pass filter on the main amplifiers is going to produce inferior results 99 times out of 100. This format exists only because if it did not the business would never be able to sell subwoofers. If crash and boom is all one is interested such is the theater crew then fine I suppose but for the accurate reproduction of bass? Not possible or perhaps highly unlikely. Listening to an acoustic bass solo such as by Ron Carter or Dave Holland you should be able to switch in an out of bypass without hearing a difference as long as a really low note is not struck. Then it will be obvious there is a subwoofer there. If there is a difference there is a problem even if you like it. If you like more bass you add it after everything is adjusted correctly.
Adjusting a subwoofer is not a straightforward process. There is choosing the right crossover slope and frequency, matching volume with the satellites and most importantly matching them in time. The bass coming from the subwoofers and the satellites has to appear sonically as if it is coming from the same instrument in time and space hopefully in phase.
Before digital bass management the only way we had of doing this was moving the subwoofers relative to the satellites which usually meant pulling them away from the walls were they performed best. One compromise after another. Does using a "swarm" system negate the need for this? Not at all. The signal from both the swarm and the satellites still has to reach your brain at the same time. Swarming smooths out the bass response within the room but this does not change the interaction with the satellites. The solution is the same regardless of the type of subwoofer system. You ping all the speakers individually and apply digital delays so that the sound of each gets to the listening position at the exact same time. Trying to do this empirically by moving speakers around? You might as well go looking for a needle in a haystack. 
I suppose many manage to reach a reasonable compromise using the tools they have but the results are far from perfect. For very critical listeners subwoofers can have a very bad reputation for this reason.
Adding bass is always fun until you realize it is making that bass drum sound like a gorilla barking. 
In short, you cannot get the very best out of subwoofers without a complete two way crossover and digital bass management. You may be able to come up with something that is reasonable but there are never any guarantees. This is the problem that lies behind the argument as to whether or not subwoofers are a good thing. For many they will not be.
For people who just want a lot of bass they will always be a good thing.
For people who want accurate low bass they can be quite the headache. That is a battle of your choice. If you get a Trinnov, Anthem or DEQX unit first you will be light years ahead on the learning curve.  

If you are using a 2 way crossover rolling the 804s off say at 100Hz 24db/oct several things happen. You will increase the headroom of the satellite system. Essentially, it now has more power to spare.
You will drop the distortion levels of the 804's woofer. Everything else that woofer carries will be much cleaner. This all assumes at least two subwoofers adjusted correctly. Subwoofers set up incorrectly will more than likely make things worse. Unfortunately, in most systems subs are set up by trial and error. Then you have to deal with room acoustics which sub performance is very sensitive to. This is an important reason why multiple subs are required. I and others seem to have landed on 4 subwoofers as optimal. Ideally, you have digital control of crossovers, EQ and time and phase alignment. You measure the sub from several points in the room and overlay the curves. Peaks or troughs present at all locations are due to the subs performance and need to be corrected. Those that vary from one place to another are due to room modes. Correcting these is a waste of power and does not make anything sound better except at one specific point in the room. It will also add distortion due to higher loads on the driver and amplifier. If the bass does not sound good at the listening position you can start EQing the bass to neutralize some of the modes at the listening position.
Without digital bass management setting up the woofer depends on somebodies interpretation of the sound. Then, trial and error adjustments with the crossover and position of the speakers. It really is hit or miss. In many instances subwoofers should be avoided.