It isn't easy finding a nice clean huge resource of free MP3's, if it were, then nobody would buy any music.
You could find a nice safe site to purchase music from, you could try Limewire (I've never had any problems with Limewire) you could rip CD's or you could try one of those search engines I gave you earlier.
Theres also ways of recording (quite easily) 'what you hear' & saving those recordings as MP3's, useful for saving songs from listening to Lost.FM etc.
What sort of bands/music do you like?
(please don't say something like boyzone... please please please)