Minecraft version 1.7.4 is out today, and this update will let you stream to Twitch with a simple key press. To set this up, you'll need to link your Twitch and Mojang accounts together, which only takes a few minutes. Just head to your Mojang account page, log in, click settings, and then you'll see an option to connect to a Twitch account.
Once you launch Minecraft, there is a new option in the menu for broadcast settings. Here you can control things like quality and bandwidth. Just hit F6 while playing, and you'll be streaming. You are also able to see Twitch chat messages along with the normal Minecraft chat.
This is a super easy way to stream Minecraft, and it's one of the best Twitch integrations I have seen in a game. I will definitely be streaming now while I play, just because it's so easy.