I will write a full length article describing how we have this setup at some point, but for now the basics are as follows:
1) a digital camcorder
2) we use a device called the cerevo liveshell (available from amazon) - which can be used to broadcast to free services like justin.tv, ustream, etc. and do what are called rtmp (real time) broadcasts to any media server. This device works great and means that you don't need a computer connected to your camera.
3) then you need a media server - we use the wowza media server on an ec2 instance from amazon. This takes a little technical know how which I'll write about when I have time, but basically it's a point and click media server.
4) then you need a player embedded in your webpage, etc. We use jwplayer for this.
Streaming live video can be very expensive if you are doing it all of the time. But for occasional broadcasts this solution is quite inexpensive. The trick is to shut down the ec2 server when you are not broadcasting (you pay for data and hours). So if it only runs a 3-5 hours a month the costs are quite low. 24 hour broadcasting would be quite expensive and running your own server would be better.
Again, I'll try to write a step-by-step article here at some point, but if you have someone with technical expertise this shouldn't be too hard to setup as there is very little configuration.