Google is currently showing a "service disruption" for Hangouts. While that may not make the outage any easier, you can take at least take some comfort in knowing you are not the only one with an issue at the moment. A recently updated Apps Status Dashboard page confirms the issues, but has yet to offer anything in terms of when a resolution can be expected.
As of the last update, which came at 12:22 PM (EST), Google has said they are "investigating reports of an issue with Google+ Hangouts." There was also mention of more information coming shortly. We had been seeing some messages come after the initial 12:22 report from Google, but that seems to have gone from bad to worse.
As of now we haven't been able to get any messages through regardless of where we try to use Hangouts. The outage has been reported on the App Status Dashboard page, however if you are in a Hangout with someone, you'll likely also notice the "isn't on Hangouts right now message" which indicates the other person is offline.
Or in this case, also experiencing the same Hangouts issue you are. With that in mind, those who rely on Hangouts for communication can take some comfort in knowing the beeps and buzzes will be stopped for a bit. Of course, we aren't sure the pleasure from the lack of beeps will be able to overtake the stress of not being able to communicate with friends, family and co-workers.
As always, you can check the current status of Hangouts, as well as many other Google services on the Apps Status Dashboard page.
[UPDATE] The Apps Status Dashboard page still lists a service disruption (as of 1:36PM EST), but we are beginning to see messages come through.