First things first. I do not endorse stealing music. This is to show how the most secure sites still have major flaws that easily allow their content to be downloaded, if you know what your doing.
Ok, so assuming you know what streaming is we can begin.
There is only two things you will need for this.
The first is Cache Viewer. Cache Viewer allows you to see the files being downloaded to your cache when you are streaming content. This can be seen in Firefox anyway by searching for your cache folder in your profile. But this addon makes it so simple.
Get it here!
The second thing you need is a website that streams audio. This also works with video but we'll stick to music for now. To find audio streaming websites you can click the Streaming link to your right and choose your favourite.
Now for the finale! When you have found your streaming site, select a song to play and open Cache Viewer. You may find it hard to find the file at first but you will pick it up quickly. The easiest way to find the file is to order by Last Fetched. As long as your not viewing loads of other sites the file should be at the top, marked Audio/MPEG under the MIME Type.
Wait for it to finish streaming then find the file. Right click it and select Save As. You should save the file as .mp3 or it will not open. Once finished simply find the song where you saved it a play it!
The biggest perk to this is the fact that the download takes as long as your internet takes to stream it, which is some cases can be a matter of seconds!
If you have any problems with this please ask and I will help you as much as I can.
Remember, downloading music without permission is illegal, I will not be held responsible for the misuse of this information.