This is a typical question where the answer changes based on time. The question has been asked in 2011, and by early 2014 sufficiently powerful x86 processors have arrived on the market that do not require active cooling.
You still need to worry about cooling the disks, which now can consume a lot more power than any other component (easily 10 W per disk, depending on the disk). This can be addressed with a good passive cooling solution, or by selecting disks that do not produce as much heat. If the case is not specially designed for passive cooling, heat will build up and if you have components producing as little as 20 W of heat, they will boil themselves to death.
There are 3 options:
- Buy an off-the-shelf solution, including disks, and be aware that you cannot swap the disks for any disks with a higher power draw. Nowadays "fanless NAS" produces quite a few good search results (and listing any model wouldn't do this answer any good a few years down the road)
- Go with external components that already have their own enclosure. Get a cheap and tiny PC (something like a ZBox PI320, ECS LIVA, or even a Raspberry Pi), and attach a couple external harddisks or RAID enclosures.
- Look for specs of the various components, such as maximum power draw, and assemble your own.