App that provides a keyboard shortcut to mute/unmute the microphone? Is anyone aware of a third-part app that provides a quick shortcut to toggle mute/unmute state of the built-in microphone?
You do not need an app for this. You can open Automator, and create a service. You can then double-click Run Applescript , and type in
on getMicrophoneVolume()
    input volume of (get volume settings)
end getMicrophoneVolume

on disableMicrophone()
    set volume input volume 0
end disableMicrophone

on enableMicrophone()
    set volume input volume 100
end enableMicrophone

if getMicrophoneVolume() is greater than 0 then
    disableMicrophone()
else
    enableMicrophone()
end if

Then save and go to System Preferences -&gt; Keyboard -&gt; Shortcuts - Services, search for the name of the Automator file, and add any shortcut you want.
More information can be found here.