Dylan has posted a good round up of the state of WebSocket support over on CometDaily.
As you can see, the browser support is limited, and the version of WebSocket supported comes into it too. The two biggest browsers, Internet Explorer and Firefox (3.x) do not support WebSocket at all. Firefox 4 beta does, but the release of that has been pushed back to 2011.
According to the wikipedia article on websockets:
It looks like websockes still has a bit of maturing to do.