I was using an old netbook (Atom N270) as a home media server, keeping it running Ubuntu Desktop 9.something. But it was too much of a pain to maintain: keeping it on mains power for a year seems to break the battery-charge-level monitoring, which makes the internal battery useless as a UPS. Too many processes insisted on writing to files every 5 minutes, which was spinning up the hard disk all the time. Also, it got uncomfortably hot with the lid closed all the time.
So I got a second-hand thin client (Via 1 GHz CPU, 1 GB internal flash drive, 1 GB RAM, gigabit ethernet) for 75 euros, installed Ubuntu Server 12.04 and a USB hard disk that has a auto spin-down feature. The 1 GiB "SSD" turned out to be too small for OS and log files, so I augmented it with a 4 GB USB thumb drive, while cursing that it is very hard to find one that performs well on lots of small writes (With 4 kB random block write tests, the throughput of most sticks is less than 0.01 MB/s). This thing takes about 13 W of power while idle (26 euros/year at our rates) and last time I looked, there are no alternatives on the market that have comparable horsepower for much less watts. The server hosts media files (MiniDLNA) and backups (snapshots) of the various computers/tablets/phones. Once or twice a year, I sync the disk with an external USB drive. If my house goes up in flames, all will be gone.
Since my media storage is mostly audio, a 1 TB drive is plenty. When I read here from people that have 40 TB of storage in NAS arrays, I wonder what they are hoarding. At 5 GB per hour of video, that's 8000 hours!
Ubuntu 12.04 server sucks for a headless server. I think it was waiting for a keypress after an unclean boot. (There was a comment on a forum of a guy who had to drive 100 miles to a datacenter to attach a keyboard and press Enter). That one was solved, but now it just hangs during filesystem checking at boot time - some bad boot-order dependency.
Network: ethernet in living room (A/V center) and work room (desktop/printer); wifi elsewhere. Visitors get the wifi password. Non-media file transfers and backups are always over ssh. (It t1urns out that the gigabit ethernet was overkill; the VIA CPU can barely saturate a 100 Mbps ethernet line, with the faster SSH cipher (arcfour).