The Mini is the perfect server for my needs. Only 12W at idle means I can keep it in an enclosed safe without overheating. In fact, I used to keep a 13W heater in there to keep sensitive belongings at room temperature, so the Mac Mini is literally acting as a heater too.
While my computers and data can be destroyed by fire or stolen, I will at least have my backups and media.
It provides 24/7 access to:
A network share for backups
iTunes server to store and serve media
DVR duty using EyeTV software and a Silicon Dust network-based tuner
FTP server to receive footage from security cameras
A secondary computer to offload handbrake queues to
I initially considered a NAS such as a Synology, but for not much more money I could get a real computer with vastly superior OS and software, thus greatly increasing flexibility and capability. In fact, I am considering running a Windows VM so I can switch DVR tasks from EyeTV to Windows Media Center (WMC has no yearly fee for scheduling data).
The other nice thing about network storage is that both Windows and OS X can read/write them with no worries about whether you are NTFS or HFS, third party drivers, OS hacks, etc.