If you fly to the United States, the Uncle Sam might take a look at your email, or bank accounts.
To be honest, I suspect that they are rather busy, and there is very little need to become paranoid just yet. As I read the story, and I could be wrong, the US merely has access to your email address, and might (if it does decide to investigate you) therefore know where to apply for search warrents.
On the other hand, I am rather amused by this silly comment by a Department of Transport spokesman:
An alternative would be simply having no European flights going to the US. It is up to the US authorities to decide what they do with the information. [emphasis added]
Is that the alternative? Is it really? Well, I suppose the Green Party would be pleased. I don’t think they thought the end of civil aviation was actually on the agenda.