Ok windows has "Windows media encoder"
http://tinyurl.com/g37zo

Mac users supposely have quicktime broadcast &
quicktime server

But then you have to get another mac, (so I've seen and heard) buy os X server... Why is that, and if I'm wrong
what's the quickest way to stream live video on my website?

You do not really need to install a streaming server. My preference is to make a Quicktime reference file (http://developer.apple.com/documentation/QuickTime/QT4WebPage/samplechap/special-11.html).