In XP you could choose the Stereo Mix in the recording sound options to record sounds as they play on the computer but I can't find this in Vista. How can I record the sounds that play on the computer and not the ones from the microphone in Vista?
Go to the windows Control Panel, open Sounds. In the Recording tab, right-click and choose Show Disabled Devices. Stereo Mix will appear (amongst other). Right-click Stereo Mix and choose Enable.
You might want to have a look at the device properties (right-click > properties) for volume and other settings.
You would probably still need to set the recording program you'll be using to use the Stereo Mix as a recording device.
One alternative is to use a recording program that supports the Vista API specifically. The Vista audio API (aka WASAPI) allows a compatible program to capture the sound that goes to your speakers. This has the same effect as selecting Stereo Mixer as your "Record" device had.
Example in Audacity:
That's all there is to it. Record Skype, websites, games - whatever. Anything that goes to your speakers, goes into Audacity too.