Unless you where trying to hack into the some goverment thing, there is not much they can do.
I have had one of my freinds have a screen with our local police logo show up saying that "YOUR IP ADDRESS HAS BEEN REPORTED TO THE POLICE".
Then again, I have seen what is on his hard drive, and i just love it how he "downloaded it by accident." And I refuse to even touch is computer because of that.
I did have a freind that got his internet cut off as "THERE WAS A COMPLAIN TO THE COPYWRIGHT COUNCIL ABOUT HIS IP ADDRESS".