Google is the big brother of all search engines. If something is uploaded into the Internet, sooner or later it will be crawled and indexed by the Google bot. This is inevitable unless there are preventive measures taken to ensure the content is not accessible to the Google bot.
Although sharing some types of MP3 files is considered illegal, there are still people who have uploaded them. We can always use Google to search for these MP3 files, provided you know the complex codes that are required. I stumbled upon two websites that enables us to easily search for MP3 files on the Internet.
Website #1: Download browser
There are four steps that you need to follow in this instruction. Just follow them and you should be fine.
Website #2: GP2
This is an easier alternative. You can search for other items apart from songs using this website.
Note: I do not recommend/advice/support illegal MP3 downloading or uploading. Not all MP3s are illegal. You can use this method to easily search for LEGAL MP3s on the Internet. Whatever you do with this knowledge is totally up to your own wisdom.