Not sure about the US, but one thing is for sure; if the US gets a cold the rest of the world sneezes. Europe may under normal circumstances be better placed to avoid a recession simply because one happens in the US, because Europe has become less dependant on trade with the US than it used to be.
But the current economic problems seem to be worldwide and stem from debt. We will all recover from it one day, depression or not. And when we do we have to make sure that we don't go down this route again. That means governments have to be honest with voters and not try to fool them into thinking they can spend an ever decreasing tax take on more and more commitments. The public do not mind paying tax if they are getting the services they voted for. We should pay for them, not borrow for them.