Hi, I have a Gigabyte GTX560 Ti OC, think it's their Windforce cooler on it, was the cheapest GTX560 anyway
As stock it's loud, the fans are thin and equivalent of 80mm fans in size and minimum speed was around 1700rpm, or maybe more, and quite noticeable, under load would get over 2500rpm, admittedly with great temps as the the under lying quad heatpipe heatsink isn't bad at all.
First step was a BIOS mod to drop the minimum fanspeed to 25%, and then 20% which made no diff to25%, this helped a good deal but...
Next step was to remove the stock fans and replace them, i used a pair of 2000rpm Sharkoon "golfballs" but any 80mm fan in this speed range would work. Fans connected to the cards 3pin fan header so it still has control of them. They take the card from 2 slot to 3 slot solution but now idles around 500rpm! As the fans are reasonable this is quieter than you'll ever hear. Under load they climb to 1200-1400 rpm but this is still quite acceptable.
With the BIOS mod allowing low fan speeds you could then also use MSI Afterburner (or the like) to redefine the fan speed curve to alter the noise/temp trade off.
So with fanswap (£10 for 2x 80mm fans) and BIOS mod it's now quieter under full load (folding@home) than used to be at idle.
I'm still going to try a Twin Turbo II on it though!
I read someone on here quoting the GTX560Ti Phantom as having 80mm fans with idle in the 1000-1200rpm range, which isn't as good as my modded card but probably better than any other GTX560Ti.
[Edit for fan speeds having looked at my notes]