FORTUNE — On April 20, 2007, a young U.S. senator named Barack Obama sent his first tweet. “Thinking we’re only one signature away from ending the war in Iraq,” the future president tweeted, a bit optimistically. Since then, governments across the world have jumped onto social media. These days, voters are as likely to see political ads in their Facebook feeds as on TV, and Twitter Q&As with elected officials have become as common as fireside chats.

But beyond the usual applications, governments are also experimenting with using social media in surprising, progressive, and sometimes just plain weird ways. I’ve seen it from the front lines working at a social media company that makes tools to connect governments and other organizations with millions of users. Specialized command centers can now monitor trends on Twitter and Facebook (FB) in minute detail, enabling officials to do everything from forecast voting patterns to anticipate disasters before they happen.

Here are 5 unusual and powerful ways governments are harnessing social media:

Picking up the trash: Anyone who’s waited all day in line at the DMV knows that government agencies aren’t always keen on customer service. But does it have to be that way? Take something as simple as weekly garbage collection. In the city of Vancouver, confusing schedules were leading to overflowing bins on streets and in homes. So the city turned to Twitter. It set up a website where residents could sign up to be tweeted the night before garbage and recycling collection. Specialized bulk tweeting and scheduling tools made it possible. Result: cleaner streets and sparkling customer service at a fraction of the cost of traditional phone centers or email.

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Defusing riots: The 2012 London Olympic Games were largely free from disturbances and disorder. Could social media have played a part? Prior to the games, U.K. police set up a dedicated social media task force. Using social media management tools, they followed known rabble rousers on Twitter, setting up streams to monitor conversations about the games and planned protests. When push came to shove, authorities were able to dialogue with antagonists in real time and, in some cases, pinpoint the exact location of troublemakers using geolocation features. All of the information was open and publicly accessible: All it took was the right tools to tap into it.

Detecting earthquakes before they happen: When a 5.9-magnitude earthquake shook the Northeast in 2011, many New Yorkers learned about it on Twitter — seconds before the shaking actually started. Tweets from people at the epicenter near Washington, D.C., outpaced the quake itself, providing a unique early warning system. (Conventional alerts, by contrast, can take two to 20 minutes to be issued.) Seeking to take advantage of these crowdsourced warnings, the U.S. Geological Survey is hard at work on TED, short for Twitter Earthquake Dispatch. It uses specialized software to gather real-time messages from Twitter, applying place, time, and keyword filters to create real-time accounts of shaking.

Preparing for the zombie apocalypse: Taking a page from Orson Welles, the Centers for Disease Control recently terrified readers with a blog post titled Preparedness 101: Zombie Apocalypse. “[Where] do zombies come from, and why do they love eating brains so much?” the author asks, before listing ways to prepare for the inevitable. The post, which also explained how to get ready for real emergencies, attracted more than 1,200 comments, with a lively debate ensuing between readers on the finer points of zombie culture and emergency preparedness. While not a social network in the strict sense of the word, the CDC blog does illustrate how governments can use online channels to engage and educate. More recent posts have focused on what the popular board game Pandemic can teach us about how disease spreads.

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Forecasting elections: During the 2012 U.S. presidential election, Twitter developed a brand new political analysis tool called the Twindex, which gauged online conversations and sentiment around Barack Obama and Mitt Romney. As election day approached — and most traditional polls had Romney pulling ahead — the Twindex showed Obama trending sharply upward in all 12 swing states. Now, it may have been pure coincidence that Obama went on to win. Or maybe not. It’s hard to dispute that buzz in the Twittersphere is tied to real-world sentiment. As analysts get better at quantifying that buzz, social media may become a crystal ball of sorts for peering into election results. Many campaigns are already investing in social media command centers, specialized software and screens for tracking social mentions, and trends in detail.

With the right social media management tools, agencies and officials are turning the torrent of social posts into a catalyst for better government (or, at least, some pretty cool apps). Keep an eye on your newsfeeds: Big data plus better software means these initiatives could be coming soon to a social network near you.