Came across the booth of this colocation and web host company that will host your Mac Mini starting at $29.99. They let you have full control of your machine through remote-control software, including rebooting. They also let you run whatever application you want. You don't get that in the Unix and Windows hosting world without paying the GDP of Uganda. This might be the solution for all you out there who want ubiquitous access to your music and porn.
Macminicolo [Official company site]