Home server Original

Please note: If you are going to run ANY services that can be accessed from the external internet, beyond the confines of your home, please secure your system per Setting up a Server.

Operating systems

You should run Debian, RHEL or CentOS if you want Linux, or any *BSD that you like.
Ubuntu usually does retarded things with their packages and versions (lib*-ubuntu1.l2), and pulls unstable software from Debian Sid.
Rolling release distros (Arch, Fedora) are not really good for a server, because it's supposed to stay working, and it shouldn't break/change it's behavior on updates.

Gentoo is usually too much trouble to be worth it, but it's ok.

You should also consider a NAS-centric operating system for a home server - FreeNAS or NAS4Free are common choices. Both are free software and have simple GUIs to set up your services.

Centralized storage

One option is to set it up with NFS (Linux-centric, can be used on windows but it's shit) or samba, so you can watch your chinese cartoons on any device and keep your documents/whatever synchronized.

You may want to consider a RAID array for long-term file storage. RAID is not backup, but will protect your files in case of drive failure. NAS4Free allows you to easily set up RAID arrays using UFS or ZFS.

Remote access

Setting up SSH access enables you to:

Tunneling

Create a tunnel and use it as a proxy for environments that block certain DNS requests or pages and to encrypt your data

Wake on lan

Turn on a pc on your lan Arch Wiki guide

Web hosting

Host webpages, use nginx or apache debian nginx guide

Proxy

You can use a proxy guide

Compression

Ziproxy (Opera style web compression, including images)

Media automation

Torrenting

Use a daemon like transmission or deluge

TV Series

You can use a daemon like Sickbeard

Movies

You can use a daemon like Couchpotato

Music

You can use a daemon like Headphones

Voip

You can use mumble-server (free), ventrilo or teamspeak (non-free)