I remembered that earlier versions of OS X had a setting for playing the mic through the speakers, but I couldn't find this anymore. It turns out after some poking around on the Apple Discussions site, that this setting now lives in the Audio MIDI Setup app in the Utilities folder. Starting this up, there are three "Thru" checkboxes next to the microphone settings at the bottom in the Audio Devices pane. Even though none of these were checked, clicking the Master one for the mic on and off fixed the problem for me on both machines.
I'm not sure which app or system update might be accidentally turning this on, but it could be related to the installation of 10.3.4, Skype, iChatUSBCam or turning on Speech Recognition. If anyone else having this problem has a clue, please post a comment.

