1. Navigate to deezer and play a tune.
2. On your local computer open the following folder:
   C:\Documents and Settings\[username]\Local Settings\Temp
   You can open it by going to Start -> Run, typing %temp% and clicking the OK button.
3. Find for a folder called plugtmp-[some_number]. You want the folder with the highest number after plugtmp- (the first and oldest plugtmp folder will have no -[number] part in the folder name).
4. You should find a bunch of files called cacheDiffusion.php or cacheDiffusion-[number].php.
5. If not, then go to the folder with the next lower number until you find the files.
6. Rename the .php file to .mp3.
7. You can now play the mp3 file with your favorite MP3 player!

For whatever reason the trick doesn't work. May be the trick works with a web-browser other than Internet Explorer or Firefox.

Obviously this trick as well as other non-working ones posted here for educational purpose only. You can use them with a service that doesn't prohibit saving music! Deezer clearly states that saving music from it is illegal!