Although you may not know it, Google is one of the best places to search for music and movies. You can use this technique to download pretty much anything. The way it works, is that google will look in index directories where people upload music for themselves or their sites.

?intitle:index.of? mp3 [artist] [title]

Put your artist name and song title in the brackets and replace mp3 with the format you like. Just type the code into the google search box and hit enter. Look for a result that matches your search and click it. Now you will see a directory with lots of music and other files in it. Find the song you want and right click > save target as, or save link as – depending on what browser you use. If you find a good directory that you want to visit again, bookmark it by pressing Ctrl + D.