The EU can still trust the US after the NSA spying scandals. The EU didn't have a lot of trust before the scandal, anyway. Most countries have espionage operations against each other. It is very likely that the EU is also spying on America. In general, countries do not trust each other.
In today's technological world everyone is spying on everyone. The US got caught more than other countries do but it doesn't change the fact that it goes on. The Union should be a bit more concerned about its privacy but it should also still trust the US because the Union is likely spying as well.
Yes, I think that even after the aftermath of the NSA spying scandal that European countries can still trust the United States' government. The NSA has been sanctioned for their bad ideas and actions, and now is the time to rebuild the relations between the USA and European countries to grow together better.
Although the US was wrong to be spying, every country has somewhat questionable methods to getting information, and the only difference between the US and other countries is that the United States got caught. The US government has an obligation to protect its citizens, and this spying was an effective way to do that, and should not be penalized for doing what is in the best interest of its citizens.
Without a doubt, the European Union can't trust the United States after the NSA spying scandals. The fact of the matter is that the country spied on its own citizens and even international allies. These same European allies shouldn't trust the United States because the U.S. has broken the bonds of trust.
At this point, the US has overstepped its boundaries and has demonstrated that it is willing to abuse its own power and capabilities, spying on not only their own citizens like this is a police state, but the citizens of other countries as well. The US will have to dismantle this program and do a lot of grovelling before they can be trusted again.
No, the European Union should not still trust the US after the NSA spying scandals, because some of the spying was against the European Union. The United States' relationship with Europe is very important, and the breadth of the NSA spying did a great deal of damage with that relationship. Europe has every right to distrust the United States.