Mojang's planned Twitch integration for Minecraft isn't finished just yet, but it's in a good enough state that you can try it out for yourself in snapshot 13w47c. To set this up, go into your Mojang account settings and link your Twitch account.
Once you have the new snapshot -- obtainable by creating a new profile and checking the "Enable experimental development snapshots" box -- and your accounts are linked, simply press the F6 key by default in Minecraft to begin streaming. To adjust settings, head into the Options menu and look for Broadcast Options. Once again, the Twitch support is in development, so expect bugs. There's a short demo above by YouTube user sethbling.
I used to be with it, but then they changed what "it" was. Now, what I'm with isn't it, and what's "it" seems weird and scary to me.