Torley Linden started this to share how he records voice chat in Second Life. This page will become more useful with additional knowledge, so please share your experiences too.
Torley Linden's method
The first key thing you'll want to check is if your computer's sound card can also record the sounds it's playing. There are a lot of variations across systems, but the option to do this is commonly called "What U Hear" (on Creative Sound Blasters) or "Stereo Mix".
I'm on a Windows PC with Realtek onboard sound, and I can enable this by going to Control Panel > Realtek HD Sound Effect Manager. In the bottom section, "Record", it appears as "Stereo Mix":
Also notice the "Mic Volume" control. If you want to record yourself speaking, you'll also need to turn this on so your headset input (your voice stream in Second Life) can be recorded.
Note: In my experience, other listeners also hear themselves talking (echo, feedback) when you're doing this. But, your final output will sound fine, so if they can put up with it and tolerate the weirdness, you can get great results.