I've just got the VPS bug. A VPS is a virtual private server, which means you get root access to a server of your choice at a very low cost (as opposed to a dedicated server).
I've managed to get some pretty cheap deals which manage services that I used to run in my house (using computers up and valuable space).
One of the servers now runs my media and another (my favourite) runs minecraft (www.monkeez.co.uk/latest-map if you're interested in the world that is being played in - note the tree house in the jungle area).
These things are very reliable and have a lot more bandwidth than my home ADSL connection, which means I can run things constantly without having to worry about the connection at home.
Currently I'm using www.buyvm.net to host a minecraft server (with all the nginx webserver in the background). They seem very stable and are easy to setup and pay for.
I'm also using another vps host (no names mentioned here) to host my media which has extremely fast connection).
Overall, this is a good way of managing services that have to run the whole time and need a lot of configuration.