Just thought I'd add my experiences...
I received my 3870 last week (a blue one, mac and PC version) and it was incredibly noisy. Fans on very high speed all the time, from cold boot. I couldn't be bothered to send it back so having found this thread, I got myself one of the Arctic cooling Accelero S1 passive cooling things and installed that.
Really simple to install if you have a screwdriver and some sort of cleaning solution for getting the old thermal paste off the GPU. The instructions that came with it are not brilliant but you can find a few videos of installing (on various vid cards) on youtube and that helped a lot (didn't find a 3870 vid but watching an install on any recent ATi card seemed similar enough).
Although the Arctic cooling thing does come with some thermal paste stuff on it, you might want to order some different stuff for a slightly neater application.
The card with just the Accelero on it is obviously completely silent which is a very joyous thing after the jet engine noise of the last few days. However, I also decided to add the turbo module fans to the top of the Accelero heatsink just to keep a bit more airflow going (the turbo module isn't much to buy anyway).
I had read somewhere about the problem of where and how to power the fans but managed to get mine powered from the old 2 pin power supply on the card. You can do this by modifying the turbo fans 3 pin socket to fit the 2 pin power on the 3870. Just snip the fans yellow wire where it emerges from the black cable sheath and tie the end away neatly with some insulation tape. Then use a sharp knife or something to slice the yellow cables socket away from the side of the 3 pin socket, leaving you with a slightly ugly two pin socket with a black and red wire emerging from it (I should say that I don't know what the yellow wire does, but the original 3870 fan was running off just a black and red wire, so I took a chance on it not being essential)
You then need to get a pair of pliers and gently pull the white piece of plastic off the two pin power prongs on the card, leaving the two prongs exposed. You can then attach your newly chopped two pin socket from the fans. Then clip the fans onto the heatsink as per the instructions. When you boot, they will spin. Mine stopped again quite soon after and I worried that they had stopped functioning. However, after a bit of COD4 or intensive Motion work, they span up to add a bit more cooling. Which was cool (and more important, still silent)
So far so good. Not sure I've explained this brilliantly, so if anyone is really interested, I could post a pic or two I guess. But the bottom line is that I now have a 3870 in an early 08 mac pro working silently via an Arctic cooling Accelero S1 rev 2 and the turbo module fans.
Would be a lot simpler if ATi could just make it work in the first place of course...