Many different sites on the internet host streaming video and audio content. Almost none of these sites will let you download the content to your local machine, but that doesn't mean it can't be captured.
Examples of just a few tube sites on the net include: youtube.com, weoh.com, vevoo.com, hulu.com.
MP3 stands for MPEG-1, Layer III (where MPEG = Motion Picture Experts Group). This is the audio portion only of MPEG-1 video. It is a popular format for compressing audio into much smaller files than those recorded on a standard CD of DVD. Thanks to the early adoption the format recieved in the 1990's it is compatible with many devices and thus enjoys incredible popularity. Of course all the compression comes at a price.
To order shrink down to much smaller sizes that its CD equavilent the mp3 file must give up some precious bytes of data. Due to the nature of this tradeoff mp3's will always be of slighty lesser quality than the original. A master of mp3 encoding can knows how to strike the proper balance between a smaller file size and greater audio quality.
Three major strategies for capturing audio streaming through your browser are: on-line capture, plug-in capture, stand alone software. In on-line capture a third party service lets you drop in a link of the requested video and will convert it for you. Most on-line services come and go quickly, this is not a reliable method of capturing audio tracks from streaming sources. Browser plug-ins share the same low reliability score as on-line capturing services. Although some can work well plug-ins are limited by the resources they are allowed to use from within a browser and like on-line services can be broken by changes made on the server side. Stand alone software solutions on the other hand function in a different way and are impervious to many of the pitfalls that ultimately render other solutions useless. Software solutions typically capture audio by recording it directly from the computers on board audio systems. This is like placing a wire tap between the source and the speaker. The program hears, and records, all transmissions. For reliability stand alone software is the method of choice.
For Windows and Linux one piece of software that works well is Audacity. (No support for this feature in OS X.)