A MacBook Air with SSD HardDisk might be what you need. No moving parts = no noise (unless you push it, of course).
BTW, I'm the same boat - I like my computers to be silent, and sold a G4 tower a few days after buying it because it was simply unbearably noisy.
I'm strongly considering an iMac presently, as a Mac Pro is a) overpriced and b) not silent enough and my MacBook Pro is quite noisy when it's either warm in the room or I feel like a little Spore. 😀

They tell me my iMac has fans, but I still don't believe it. Occasionally you'll hear a little sound when the hard drive does something, but mine is otherwise dead quiet.
+1 Can't heard the machine even if I try. iStat says I have fans, and they are running at 1200 rpm, but I can't hear them.
(FWIW- 24" 3.08 gHz iMac with NVIDIA GeForce 8800 GS)
My imac has a noticable hum coming from bottom left. Its not extremely loud, but is louder than for example my BT vision box when it is on standby. (for anyone who has BT vision.)
Do you think I should send in my iMac to get it looked at? The iMacs at my school all seem pretty silent aswell.
You could try, however I doubt that it will change. If you look up the technical specs for the iMac from the Apple website the iMacs are rated with some low 20db figure at light load. This is a low number for a typical office or school environment. However at home in in a quiet setting this will be quite noticeable.
If you look at some of the photos from people disassembling their iMac you will see that at the lower left there is a big fan that sucks in the air for cooling of the unit.
I had Apple changing the fan in my iMac since a lot of people told me that their iMac is really, really, absolutely dead silent. It did not make a difference. The fan can be heard quite the same. I now have come to accept it and maybe there are dead quiet machines out there or people live in areas with higher background noise than I or maybe prolonged listening to maxed out iPods has somehow impaired their hearing - I don't know.
If somebody with an absolutely, dead quiet machine lives somewhere near Berlin, Germany, I would like to ask if I could check out their machine. So far even all the Apple people told me that I can not expect it to be COMPLETELY silent.
Thanks, Thats the sort of answer I'm after. I feel very skeptical of anyone who claims to have a dead silent iMac. Im going to go check out my school iMacs tomorrow, they have 12 new ones and 6 old ones. I guess that should tell me the definite answer.
I have the 24" 3.06thing, with a 8800 card and a 750gig hdd.
It is not silent, there is always a fairly audible fan going. It may be the HDD. It is a PITA. It can be heard across the room. It is very disappointing.
When I got it at first, it was absolutely dead silent. Nothing was audible. Then it went noisey after a month. Fan running all the time at 1200rpm. Took it back, it was replaced, but the replacement was instantly noisy. I didn't take the 2nd one back as it's a chore to lug it back to the store.
Maybe the 500gig would have been silent. Don't feel I've wasted my money, but having use previous iMac without a sound, I feel the recent 24" alu's are a step backwards.
Best of luck
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NB: Are there really dead-silent computers anywhere nowadays, besides the netbooks? Even the laptops have fans.
I've been worried about my 2.8, 24" iMac for a few weeks now.
It's relatively loud and I think it's the hard drive making all of the noise.
It started off dead silent, but now I can hear it 'reading the hard drive' anytime it's on.
I had the same issue with my old MacBook which was replaced (also had screen flickering problem).
The screen on my iMac has that uh...black uneven-ness that people have mentioned time and time again on this forum. It's very noticeable. I'll post pictures if I can later.
Would you guys care if your iMac had the aforementioned issues? I don't know if I should report it to Apple Care since I really doubt they'll be able to 'fix' anything.