I want to build a home server mainly to store and serve files. I might use it for other things, but it will not do heavy tasks (such as video decoding for example) so the processor speed is not my greatest concern, but I want it to be really silent so a fanless system would be ideal. I was leaning towards an Atom, such as the n270 or the D510, but I noticed that they don't support ECC RAM. I am not sure yet if this is an essential requirement for my home use, but I am interest to know what alternatives do I have. Do the AMD Fusion processors support ECC? And what about VIA? I am open to suggestions.

Thanks

Other AMD models support ECC RAM. If you underclock them enough, you can run them without a fan (undervolting is nice but hardly needed and could easily compromise the stability).
That's what HP did with their Microserver. There's a case fan but it doesn't blow on the CPU which has no heatsink fan.

Thanks for your answer. Do you have any specific recommendation? I never over/underclocked anything before, but I should be able to figure it out.

Other than the Microserver, not really.
Ideally, you'd use mobile gear but the problem is that the board and the BIOS must support it. If you can find such a board for less money than a whole Microserver, great. Don't forget to tell us!

Asus has ECC support on some of its consumer desktop boards (or used to anyway) and good features. But power consumption tends to be high. Add the cheapest low-power version among AMD dual-cores and underclock it further. Put a huge heatsink suited for fanless operation like the HR-01 on it (see SPCR's recommendations) and pray. Hopefully your temperatures will be acceptable. Maybe add or upgrade heatsinks on the motherboard if other components get excessively hot.

I wouldn't go down that road.
Instead I would forget about cheap gear and pay the price Intel demands for proper server gear: S1200 variant + 1220L or 1225 (if you want the GPU). Power consumption should be better than with mainstream AMD gear (at least as far as the CPU is concerned). You should get more reliability out of that than consumer parts. Maybe not but that's your best shot.
If that's too expensive, maybe look at which Intel consumer CPUs support ECC (Clarkdales apparently do for instance) and find a matching Intel server board (second-hand if need be). Intel boards are your best best for low power consumption I think. edit: according to a quick google, the sandy bridge dual-cores may support ECC (but don't take my word for it!). In that case a cheapo like the G620T or the G530T would be a good alternative to the 1225 and your best bet for low power consumption at a decent price.

Alternatively, you can wait for the new AMD Opterons; according to the leaked info, there is a 35W variant in the new line-up, priced around $120. Availability expected before the of the year.
Some thoughts from somebody who's in researching for NAS: look at the NAS as infrastructure; it doesn't has to be high-powered, but it has to be reliable. An Opteron or Xeon will serve you long time, well over the warranty period. I definitely will go with ECC, even if that means $200 more, but I can expect to serve me as long my gigabit network exist.

A fanless Opteron would be something to behold. Don't mind the ratings. Intel is where it's at for power consumption. AMD makes good niche gear but its mainstream gear can't keep up with Intel.