In the US, you are contractually responsible for whatever is done with your connection. But that's not a legal distinction. You might be throttled or disconnected, but you won't get a criminal record.
Edit: in some ways it's worse because there are no courts involved, so there is not always any reasonable way to defend yourself.
JTR is a bit of a special case though.. she willfully and knowingly infringed copyrights (and this has been affirmed through at least 4 appeals that I know of).
The MafiAA knows they'll never get that judgement.. it's just to make a point. Besides that, any decent court will allow you to work out a payment plan. (I say this as someone who has been sued for absurd amounts of money before!)
It's annoying, unethical, disgusting, and a lot of other mean things, but hardly life ruining.
Edit: in some ways it's worse because there are no courts involved, so there is not always any reasonable way to defend yourself.