Kinda hard to explain it all in a little post like this... keep in mind there are people who make their living dealing with how the exhaust sounds. I've done a few myself... Ford T-bird, 2001 Harley Edition F150, and others.
Everything mentioned will make a difference. Anything that changes the power of the engine will also change the sound. Simply changing the timing can change the sound.
Manifolds play a big part in the sound. If you analyze the sound, the results are typically tied to engine orders. A V8 fires four times per rev, so (assuming it's an even firing engine) fourth order is often dominant. But, if you have unequal length downpipes, or uneven firing intervals (i.e. Harley Davidson) you will create "odd" orders, which some people think sound powerful. Typically "even" orders sound smoother than "odd" orders...
In general, small pipes filter out low frequencies more than larger pipes do. Long pipe lengths can add drones to the exhaust note, this typically gets worse as the pipe diameter goes up. One thing to keep in mind - mufflers don't do anything other than filter sound. If the engine isn't making the sound to begin with, a muffler can't add it in.
And of course there are exceptions to about everything I've mentioned, but like I said, people make careers out of this so you can't get it all in one post... Plus, sound is subjective. Different people perceive things differently so what sounds nice to me may sound weak to you.
Oh yeah, last comment. For the record, I think loud pipes suck.