I do daily recording of streaming audio from the BBC Radio 4 streaming audio website, and over the years I have found absolutely the best software to use to be the freebie Audacity.
In Windows 7 you may need to enable Stereo Mix as this is usually disabled by default (to discourage music piracy, apparently). Audacity is fairly easy to use and also enables any flaws to be tidied up after recording before saving to virtually any chosen format, e.g. MP3 at whatever bitrate suits you best.
There are several other freebie apps out there for recording streaming audio, but few have the flexibility and the clean-up options Audacity offers.
VLC is of course better and simpler than Audacity for actual playback, though Audacity can be used for this.