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Google Analytics has been an extremely helpful tool. Especially now with the introduction of the Real-Time beta. The Real-Time beta gives you a number of how many people are on your site currently, what page they are viewing, where they are, what they are viewing it on and more. To me I believe there is an incredible amount of possibility with real-time interaction. An article from Link-Assistant.com suggests three uses that where not possible without the new Real-Time beta. 
1) Immediate react to traffic drops.
2)Chase trendy content for immediate community engagement
3)Plugging in to important discussions

One thing that would work as well is knowing your audience during a live feed. If your feed is picking up momentum in a certain part of the world maybe taylor it to that,  or if it is starting to drop in viewership you can immediately react and make it more engaging via social networking or Twitter comments or questions.

Along with 2012 came many more upgrades to Google Analytics. You can get a quick overview of the other new features here.