"On my XP machine if I hear something I want to record, I bring up Accessories, Recorder. Then I hit the Record button and [it] starts recording all of the sound going to the speakers.
Blame Microsoft, Ken (I always do). For whatever reason, Vista lacks some of XP's audio-recording capabilities. Fortunately, there are several third-party solutions.
Just the other day I used one-Free Sound Recorder-to capture a new Brendan Benson song from a site that was streaming it. (Don't worry, Brendan: I plan to buy your new album come August, just like I bought all the previous ones.)
The app's pretty easy to use, though I did need to follow the Vista-specific instructions to enable Stereo Mix in Vista's Sound settings. From there you just click the Record button (or hit F9) to start recording whatever audio you hear through your PC speakers.
If you want more of a browser-based solution, check out Applian's Ask & Record Toolbar. True to its name, it's a toolbar that adds audio-recording controls to your browser. (Thankfully, you can decline its request to make Ask your default search engine.)