There's Media Source Extensions, but it's a draft standard with limited support currently.

I also kept Flash around mainly for this reason. It doesn't help people that want to make streaming video sites, but you don't need Flash to watch live video streams from sites like twitch.tv. You just need a media player capable of playing streaming video (mpc-hc, mpv, and vlc all work), and the livestreamer command line tool which extracts direct video stream URLs from twitch.tv pages.

http://livestreamer.readthedocs.org/

This works perfectly for me, arguably better than the Flash-based player. I uninstalled Flash a few months ago and haven't felt the need since.