Freecorder, which records to MP3 files. It's from Applian Technologies, whose blurb says: "Freecorder does exactly as it sounds -- it is an easy-to-use FREE software program that lets you record sounds on your PC. The benefits: Records what you hear from your speakers. Saves recordings as MP3 files. Easy to use. BONUS: Record Skype™ Phone Calls."
There's a more advanced full version of this sound recorder, but you can download the basic version (which they make available as a "demo") for free.
It's very easy to use, as they claim. Click the Record button to start recording; if necessary start playing whatever it is you want to record (remember it just records what's being played via your PC speakers); click Stop when it's over or you want to stop recording; and name and save the resulting MP3 file (if it's set to prompt you for the filename after recording), and that's it. Though it's dead easy to use they also provide a helpful screencast (though some of the features mentioned are disabled in the free version), plus user guide including step by step instructions/tutorial, and decent support pages generally.
The main thing to watch is the settings, see below - it takes you through the settings when you first launch it, and you need to choose the correct sound card from the dropdown (for some reason mine defaulted to something peculiar so it recorded nothing until I cottoned on and changed it). I also chose to Prompt for File Name After Recording as I thought that was more convenient. Haven't tried recording Skype VOIP calls over the Net yet, but I would be surprised if it didn't work.
There are limitations to the freeware version, which shows ads. You can only record at 64 kbps not 128 kbps, i.e. the recordings are of lower quality. You can't pause a recording, you have to let it run (though you could edit it later with the free Audacity). You can't tick "Eliminate silence" to get rid of silences from your recordings, and it records for only 30 minutes at a time generally (or 2 mins for Skype or other VOIP calls, according to their site). You can't get it to automatically name files with a time stamp or add title tags to MP3s either (though again you can add tags to the MP3s later with other software). You can of course have all that and other features if you upgrade for US$19.95 which, if you do a lot of recording of Net radio shows and the like, is I think well worth it for what you'd get.
If you wonder what the "Advanced Recording Options" in the Settings are (Record internet radio shows, streaming music, streaming video) though, so do I. Clicking those just opens a blank browser window, for me. I suspect from the Freecorder user guide that they're just to ads for other programs by Applian designed to record internet radio, etc. You can of course record short lengths of streaming music using Freecorder Basic anyway.
Yes, there's other free software (like the open source Audacity) which will record streaming music, or whatever music or audio is being played on your speaker, too. But this is a nice, simple single-function program, and I do like the elegance of single purpose tools that do whatever it is they do easily and well, especially when they're well-explained, well-supported and free (like the free audio file converter NHC Switch which I reviewed a while back).