http://www.hunt4tunes.com/ - think you can even search specific sites, although I'm guessing MegaUpload is redundant nowadays.
Use file sharing services (some still exist)))) which have search options for that purpose. lady_novalia is right 4shared.com is o'k. There are also file storage search engines - FileTram.com and FilesTube.com. You can search there.
Dear Simpson... google is not only the best engine it is also a number one engine that gives a relevant result to our search.....GOOGLE BEST
Google, other dedicated mp3 search engines dont last that long. (filestube & 4shared are good as an alternative)
You can also use mIRC if you know the right server and channel. A lot of users share their mp3s on it.
Don't confuse yourself with boaring search. Use Soulseek. It is a perfect free p2p client and you will find there any music you wish. You can learn of what bitrate is the song you download, you will enjoy chatrooms dedicated to many music styles. And many many other stuff.