Almost any case can be made to run quietly...you just have to limit the amount of fans you have installed and make sure you have a power supply that is known to run quietly (the newer Antecs and Enermax power supplies operate very quietly).
You do need at least 1 case fan installed (on the back for exhaust) but it doesn't have to be a high RPM screamer. Look for fans with low RPMs and you'll reduce the amount of noise your computer makes. Panaflo, Pabst, Sunon, NMB, Vantec all make low RPM case fans that run quietly.
You do want to pick out a good case that is fairly sturdy with fairly thick sheet metal...the cheap cases come with really thin, flimsy sheet metal and I think this only helps to amplify the vibration noise from case fans.
Cricket