The last couple times I've tried to have a Google Hangout from my desktop computer, we have had audio problems. Specifically, the other people could hear me just fine, but I couldn't hear them. The "test" button in the Hangouts settings produced sound just fine, and other applications produced sound. The last time this happened I resorted to joining the call from both my computer (for video and screen-sharing) and my phone (for audio). That felt stupid. I had previously used Hangouts on this computer just fine.
Tonight I got Dani's help (needed another call participant) while I tried to debug it. Same symptoms and no bright ideas. (We tried the phone thing; that worked fine again.) This time my searches led me to this thread, where I saw that somebody else solved the problem by using a different browser. Specifically, Safari.
I was using Chrome, figuring that Google's browser and Google's conferencing application ought to play well together. But nooooo, that was a mistake. I don't know whether the fault lies with Google or Apple, but sheesh! (No, there was nothing relevant in my Chrome settings. Chrome offers to prevent sites from using your input devices, like your camera or microphone, but this was output.) Switching to Safari worked, after I installed and enabled a plugin.
I suspect that, the last time it worked, I was using Firefox instead of Chrome and that made the difference. But once I found a solution I stopped taking up Dani's time with experiments, so I haven't tested.
WTF is wrong with Chrome + Hangouts + Mac? I found lots of other people who had this problem; it's not just me.