I suppose it depends if we are talking about a criminal or civil case. AFAIK in a civil case (say copyright infringement) they simply have to prove that it was

I suppose it depends if we are talking about a criminal or civil case. AFAIK in a civil case (say copyright infringement) they simply have to prove that it was likely to be you or that your negligence (i.e opening up your internet connection) aided somebody else. It's certainly enough of a gray area that I wouldn't want to get involved.