By law a Federal representative (in the U.S.) or someone from the cable company acting unbiased towards the situation has to monitor the amount of traffic traveling to each of your modems. If they notice an that you are downloading music or any copyrighted materials, then by law your ISP is suppose to send you a letter stating that you are to stop downloading or they have the privilege to stop your service.
Typically it doesn't go that far. the DRM wants the money first and by then the party probably can't afford the internet. From what I heard, they don't really worry about your downloading habits unless it totals $2000 - 2500 or more in damages.http://www.copyright.gov/legislation/dmca.pdf
Yes I have downloaded music illegally before, but have changed my ways since people started to get fined. I really like iTunes in the fact that you can preview the music before downloading it. Then if I'm not sure I don't have to pay the 99 cents. Besides it works for me because there were just too many albums I bought as a teenager that the only good song on there was the one I wanted the album for.
Some ISPs do not follow the law though. Even after people first started getting slapped for fines, one local ISP never slapped a friend of mine.