What would happen if you get caught with mp3 files on your computer?

Nothing. MP3 files are a perfectly legal file format. You can even purchase music in MP3 format from sites like Amazon MP3 or on Wal-Mart's online store. In order for you to be prosecuted, it would need to be proved that you downloaded them illegally, as opposed to purchasing them on a legal music site or ripping them from a CD.