Does the HTML5 video element support non-HTTP-based (HLS, SmoothStreaming, etc.) live-streaming protocols?
Does it support RTP/RTSP streaming protocols? Does it support RTMP? Are there specific browsers that support or don't support it?
HTML5 tag has very limited support on video sources. The video sources supported are also limited to what browser your visitors use. Please see:
http://www.w3schools.com/html/html5_video.asp
for a table of supported formats depending on browser. To sum it up, HTML5 Video supports MP4 on all browsers and OGG, WEBM in FireFox, Opera and Chrome. With that said, it is Technically Possible to stream RTSP/RTP, but highly unrecommended.
If you must use HTML5 Video and have more control over the streaming server, you could try This Solution, which explains how to stream a video through an ogg file with VLC. Then that ogg file link can be used to stream the video on a page with HTML5 Video Tag.
Alternatives to HTML5 Video tag
Flash Video Players support quite a bit more then HTML5 Video. For example JW Player supports:
And for even more advanced video and audio source support you could try VLC Web Plugin, or the new WebChimera (based on libvlc). (both of these require a plugin installed, flash requires a plugin too, but that is usually already installed)
UPDATE
As NPAPI plugins have been deprecated in most browsers, using VLC Web Plugin and WebChimera NPAPI is no longer a solution.
Another interesting thing to note on this topic is Dailymotion's HLS.js that gives the possibility of live streaming to all browsers through HLS.