Apparently, it's not too difficult (at a very rudimentary level) to record a visitor's audio from a website, but I'd rather get some existing software to do this, rather than cobble something from absolute scratch.
What about jRecorder or a Flash-based method by Sajith Amma? I sort-of would like to avoid having to run a special media server, especially at the beginning, when I'm just using off-the-shelf retail-level web hosting.
I've tried the following searches, (all without the quotes); maybe you can think of others, (please)? "flash record audio", "flash audio recorder", "audio recorder online", "voice recording flash", "voice recording web", "voice recording online".
Looks like JavaSonics ListenUp used to be a possibility, except that they're no longer selling it. (Is this a rogue copy?) How about the open-source wami-recorder? Barebones Audio Recorder? I'll probably go with Audior anyway, since their product does look pretty good, but still, I'd be more comfortable if they had at least one real competitor.