The Wii is very quiet. A fan can be heard if the room is very quiet and you put your ear beside the console but it hardly makes any noise. It is far, far quieter than my 360 - like comparing a whisper to a megaphone.
I know what you mean about the noise of the Xbox 360. I've got one and it is very loud !
The Wii is much much quieter. The only sound I hear from it is the CD spinning - but if you don't have a CD in the machine then I can't hear it at all.