I think the careful selection of components can help this more than any case. My suggestion would be to shop for things that are specifically quiet. I went for the option of having lots of big, but relatively slow spinning fans, that way I move lots of air but without any audible noise.
I run a Corsair 400r as the case, with the two front fans running at max speed constantly. I moved the standard rear exhaust fan to the side intake position and run this at about 1000rpm, set on a curve up to it's full 1200 as the cpu temp increases. Even at 1200rpm this is pretty quiet.
I then have 3 of these
http://www.overclockers.co.uk/showproduct.php?prodid=FG-003-XG&groupid=701&catid=2331 as exhausts in the roof and rear. Using the motherboard software I run them at about 600rpm the vast majority of the time and again these will ramp up as the CPU temp increases. Luckily the fan expert software lets you control the fan curves and the speed at which they raise up and down, by making sure the changes happen slowly even when they do ramp up you dont get the sudden change in fan noise so it's hard to tell.
I also have one of these cooling the CPU again set so the fans run slowly.
http://www.overclockers.co.uk/showproduct.php?prodid=HS-020-AL&groupid=701&catid=2330&subcat=2337 At idle they spin at about 600 rpm, again upping as the CPU temp changes.
One of the biggest areas I was able to reduce noise was by picking my PSU closely. I run the Corsair AX760, this doesnt need to turn it's fan on until your pulling something like 500W+, as my entire system never exceeds that wattage it never turns its fan on effectively making it silent.
I also picked my graphics cards carefully making sure it was a quiet cooler design. The twin frozr on the MSI cards is basically inaudible at idle settings.
In short the loudest part of my case are the front two intake fans, but even those are quieter than just the fan in my old PSU was before I upgraded. It's in no way silent but unless you need to sleep in the same room you would never notice. Even the quietest of music or game noises completley drowns out the sound made by the PC and this was mainly achieved just by carefully controlling the fans.