I cannot hear it at all over my case fans and I would say my pc is fairly quiet. When playing BF3 it gets fairly warm but it's still silent. I should add that I had a Gigabyte 560ti windforce with apparently 2 silent fans and I could hear that while gaming.
I based my decision off this review (only one i could find at the time):http://www.fudzilla.com/home/item/27432-evga-gtx-670-ftw-reviewed/27432-evga-gtx-670-ftw-reviewed
"Thermals and Noise
EVGA did a great job taking the GTX 680’s design for its GTX 670 FTW graphics card. The fan is silent in idle mode but even when it’s under full load you won’t hear it until you’re really close to the computer. Bear in mind that the GPU was overclocked from 915MHz to 1006MHz and that the cooler is still silent. In fact, this is the best GTX 670 cooling solution we’ve tested so far."