There is a continuum between "keep track of what you happen to see", to "penetrate networks and install bugs", to "recruiting human agents in their government" and beyond. It's in general the job of agencies like the NSA to keep track of all foreign governments, but the degree of escalation and hostility is a political decision and not a technical one.
If the US government has decided to treat the EU as an adversary, it doesn't exactly bode well for, eg, NATO cooperation, or access to the EU market for trade (particularly in computer services). If the NSA is doing this simply because they have the ability, then they're usurping decisions that properly belong to the democratically elected civil government, such as it is.
I'm pretty sure we'll know in time that the US and Britain were behind some Euro manipulation too. The EU is right now like a big blob of countries. Some of the sovereignty was handed over to it, but its a lame duck when needs protecting itself. But then, when it does act, it acts against its members countries, and not to protect it form outside.
If the US government has decided to treat the EU as an adversary, it doesn't exactly bode well for, eg, NATO cooperation, or access to the EU market for trade (particularly in computer services). If the NSA is doing this simply because they have the ability, then they're usurping decisions that properly belong to the democratically elected civil government, such as it is.