If you have the Stereo Mix (could be called System Mixer) as the default Windows system recording device, then you can use just about any recording program that will record from the Stereo Mix, such as the free Audacity.
Computer type PC/Desktop System Manufacturer/Model Number My Own Build OS Windows 7, 64 bit Home SP1, Win 8 Pro 64 bit CPU Intel i7 3770 Motherboard Gigabyte GA-Z77X-UD5H Memory 16GB GSkill Ripsaw F3-14900CL9Q-16GBXL Graphics Card Sapphire HD7770 Sound Card RealTek Monitor(s) Displays Viewsonic VA2448 Series 24" LED Screen Resolution 1920X1080
Keyboard Kensington wired Mouse Logitech Wireless PSU Antec High Current Gamer HCG-620M Modular Case Coolermaster HAF XM Cooling Corsair H80 Liquid cooling with aftermarket Nexus quiet fans Hard Drives 240GB Intel 520 SSD for Win 7
128GB OCZ Vertex 4 SSD for Win 8
1 TB Seagate drive for backup Internet Speed 40 MB/sec (Cable) Antivirus Microsoft Security Essentials and Malwarebytes Browser I.E9/Firefox Other Info Sonar X2 Professional 64 bit Recording Software with Roland Octa-Capture and MAudio Fast Track Ultra 8R recording interfaces, Frontier Tranzport wireless control unit, Behringer BCF2000 Control Surface.
Five USB connected optical drives for CD Audio production using Nero 11
Other systems: Desktop with i5 3550 CPU, LenovoZ560 Laptop with Win 7 64 bit HP, SP1, new iPad
Winamp has it's own out of the box Nullsoft Disk Writer plug-in. The only problem I see with it: this plug-in produces raw data or wav files without compression. Thus, instead 6 megs mp3 you will get 33 megs wav file.
Actually you can do it without any plug-in to record music. some program like Leawo Music Recorder. But it only works on mac pc. It can record on YouTube, Last.FM, Pandora, Napster, Spotify, GUBA, NPC, MySpace, archive.org, BBC Radio Audio, iTunes Radio, RTVE, Sirius Radio, Radio Blog Club, XM Radio Online, AOL Music, etc. I don't know whether it will work on Winamp, you can give it a try.