There are a few plugins for Moodle that support capturing a computer’s microphone or webcam like Poodll and Youtube Anywhere. Babelium is an open source project and it’s Moodle integration is an additional resource if you’re looking to have students record audio or audio and video as an assignment submission in Moodle. A few use cases suggested by the addon maintainers: students can dub roles, be recorded reading aloud, have an interactive chat, discuss a topic from the course, and more.
The assignment plugin is available for Moodle 1.9, 2.0 and 2.4+. You can give it a test drive at http://moodle.babeliumproject.com/. In one example on the demo site that I was able to check out, students watch a video and narrate the audio of a short animation (pretty slick).
Babelium’s short video is embedded below [direct link: https://www.youtube.com/watch?v=FI2R2iXS5HQ]