Is it possible to listen to any kind of internet radio with HTML5 directly? I mean is it posible to play live mp3 streams in HTML5 complaint browsers?
Yes, it is.
Take a look at the former specification of html5: http://www.whatwg.org/specs/web-apps/current-work/multipage/video.html#attr-media-src
There is a huge load of specialities about streaming in html5.
And furthermore, take a look at this: http://web.psung.name/zeya/ - a whole html5 media server.
EDIT
Actually it's like impossible to stream live media. It's not that it'll stay impossible, but actually it isn't implemented at all - well none of the today's HTML5 browsers are going to support this in the next month's, because the real "live-stream", as known from flash (or equal) hasn't really been specified by the w3-committee - yet.
2. EDIT
As previous experiments showed, it may be possible to use streams without explicitly implement something specific for them. The "non"-stream way works on both streams and static files.