Some years ago managing a server at home was something geeky, something for hackers who wanted to control a web server. Now the evolution of the high tech goes toward the buzz word "Cloud Computing" whatever it means to You, it will involve also the non professional consumer because the data are moving from the Personal Computer to a multitude of devices like tablet, smartphone or media center.
Often Cloud Computing means services, You can choose to run Microsoft Office, Libre Office (the new OpenOffice.org) or Google Docs, You can own phisically a server or You can buy a remote one (per year or for the time You use it). It depends which is the layer You want to control.
Now lets see some cool reasons why You should consider to manage an home server.
The control and Your Privacy
When you use an external service, You can't control really your data, somebody at Google could read your data, your search queries without your permission and without You will be ever notified. Yes you could add some cryptography on top of your data but it will be harder to access to this data when You are not with your PC (in this case HTTPS could protect the connection but it doesn't protect your data on the remote server).
The hardware is cheap and fanless
There is a prototype that will cost just 25$/35$ (Raspberry Pi), it runs Linux and the power usage is very low 2.5Watt. There is another interesting project: Pandaboard that will be officially supported by Ubuntu ARM.
Continuos Data Backup
Services like Dropbox are very cool, but if You want to store more data you have to pay and You will need also a lot of bandwith and a fast connection. An Home computer server based on a SoC (System on a Chip) Computer can do it with open source software like Sparkleshare.
App and System Backup
An "alwais on" low power pc could run OS specific software for the OS. So You could backup Time Machine without an expensive time capsule.
Share Your Music or Movies via local streaming
Via the protocol upnp or Samba you can stream your media files over the network and many software for torrent ed2k or torrent offers a web gui to manage the software via browser.
Share your Printer across the LAN network
Often the network model of you printer is more expensive than the basic model plus a SoC.
Share the files across the LAN (and Internet)
You won't be worried anymore about big email attachments rejected with timeout or because the excessive size, because You could send a link to a specific file uploaded in your server to somebody else. OwnCloud.
And at the end an home server could also be used for home automation (in conjunction with Arduino) or as storage for a network webcam.
Some other Links: