There are two types of quiet cases.
1. Those that use case designs to maximize airflow using a lower number of fans (antec sonata series for example)
2.Those that use padding in the case to dampen the sound (P180 for example).
I have the Sonata II case and love it. You can't tell from the pictures on the net, but the case is gorgeous. High gloss black finish, it is like having an elegant grand piano sitting on my desk.
Anyways, it's designed to use only one 12 inch fan on the case plus the fan on the PSU, both designed to be quiet. There are no fans on the front of the case to draw air in. This is why the case is so quiet, it uses less fans, and the fans it DOES use are quiet. The drawback of these cases is that they are not really the best selection if you plan on overclocking or setting up a crossfire/sli setup for example, as the cases are not that good at cooling. They are fine for normal use though. I have an Athlon64 3700+, a 7800GT etc in mine and my temps are excellent.
Note that with these types of cases, your "quiet" system is limited to the noisiest part of your computer. In my case, my graphics card is a fairly noisy one (I have the Asus En7800GT).
If you go for the type 2 case, like the Antec P180, you are going to pay a little more, but they are nice. I built a system with the P180 a few weeks back and they are sweet. Here, cooling is not a problem at all with 3 big fans in the case. These cases have special padding built into the walls to dampen the noise.
Hope this helps. Good luck!