The most POPULAR stream recording software (free download):

• REPLAY MEDIA CATCHER
  the best audio/video stream ripper. Supports the most popular flash video format (RTMP and HTTP).
• REPLAY CAPTURE SUITE
  the best audio/video stream recording/capturing bundle
• REPLAY MUSIC
  the best streaming music recorder
• WM RECORDER
  the best Windows Media, Real Audio/Video stream capture software

Other RECOMMENDED software and services:

• REPLAY MEDIA GUIDE
  free service to find and record online radio, Internet TV, podcasts
• AVS VIDEO TOOLS
  convert, split, join, remove commercials, edit, rotate, apply effects, capture, transfer, copy, rip and burn DVD and video files
• EMUSIC
  the best legal music download service
• AUDIBLE
  download audio books, audio magazines, newspapers, radio programs
• SOUNDTAXI
  remove DRM protection from Windows Media, iTunes music and video files

See also SHOUTcast video and audio rippers for more software allowing to record Winamp video streams (.nsv) and audio streams (.mp3)

• RMBSoft AudioStreamer ($39,95/Windows) while listening to your radio station, you can record them. All recordings can be saved as individual tracks, and AudioStreamer automatically adds the correct MP3 (artist name, song name, ...) tag to the recording.
  You can browse through the radio stations, selecting a genre and the preferred bandwidth. You can also search for stations by keyword. The recording library shows you all your recordings, sorted by Genre or Radio station. Rename file(s), change or view MP3 Tag info for every file, or play the files you recorded earlier. You can also add your favorite station to the Favorites list.
  Download AudioStreamer
  Buy AudioStreamer at RegNow for $39,95

• Twins Stream Ripper ($15/Windows) - allows you to connect to various SHOUTcast compatible servers/broadcasters and save the streaming audio. Twins Stream Ripper can record SHOUTcast audio streams, making a new mp3 file for each song. You can also add radiostations to the favorite list.
  Buy Stream Ripper at RegNow for $15

• RipCast Streaming Audio Ripper ($17.95/Windows) allows you to connect to various SHOUTcast compatible servers/broadcasters and save the streaming audio to one or more MP3 files. This program even has the smarts to save each song as a separate MP3, rather than saving them all as a single file. RipCast comes with RipCast Agent, a utility that allows you to easily download from streams you find in your Web browser. It also builds and organizes your MP3 collection with an easy-to-use interface and allows you to browse for the type of music you like.

• AudioXtract (Shareware/Windows) lets you receive and record thousands of streaming SHOUTcast internet radio stations on your PC - just like a VCR. Free trial version allows you to get 100 free MP3s!

• BOOMBox Internet Radio Player (Free/Windows) - allows you to connect to various SHOUTcast compatible servers/broadcasters and save the streaming audio. BOOMbox can record SHOUTcast audio streams, allowing you to set when the program will stop, how it should cut the song, and song change detection to keep each song in its own mp3 file. You can also search for stations by keyword. You can also add radiostations to the favorite list.

• StationRipper (Free/Windows) - allows you to record up to 200 SHOUTcast internet radio stations at one time. This program can get a list of available Shoutcast stations and start recording them, creating a single MP3 file for each song the station plays. You can schedule recordings, skip already recorded tracks.

• Mp3 Stream Recorder (Free/Windows) - allows you to record live mp3 streams. It can split stream into multiple tracks.