Yes and No. It is possible to set up a Shoutcast server on your home computer, however with the usual 256kbps upload speed, you would be able to just about support 3 or 4 listeners at 64k. If you need to support more listeners, then you will need to either upgrade your Internet connection (expensive), rent or buy a dedicated server and have it installed in a data centre somewhere (very expensive) or buy a streaming server from a Shoutcast host - that's us!
Our servers all come with a 100Mbit/s Internet connection which enables us to host a number of Shoutcast streams on each. The savings made from buying bandwidth in bulk are passed on to the customer.