What type of thread are you using, and what size needle? Often this is a problem involving a mismatch of needle size and thread type.
I also highly recommend watching this video by Jamie Wallen:
http://www.youtube.com/watch?v=Q1mRhcquZTM
Adjusting the bobbin tension to as loose as possible, then adjusting the top tension until you get a balanced stitch, helped me a lot when I had shredding/breakage issues. The other thing that helped me enormously was switching to Glide thread. It *never* shreds or breaks on me!