There is also a Safe Harbor scheme that is intended to overcome this problem so working with US businesses is still possible if they provide additional safeguards. However, it's now clear that no business operating in the United States can actually offer the required guarantees, no matter how sincerely they might wish to. It is therefore unclear whether a European business relying on Safe Harbor to cover its rear would actually have much of a case in court if one of its customers were actually damaged as a result.
I've seen a lot of businesses at least considering pulling out of US services, cloud or otherwise, for this reason in recent months. Some are sticking with it, on the grounds that there is safety in numbers: no government regulator really wants to damage global trade by making examples of businesses who are just trying to do their work and acting in good faith, and if you're dealing with a similarly honest business from the US then the odds of an actual customer complaint are probably low enough that it might be considered an acceptable business risk. Others seem to have lawyers who are more wary and fear the penalties of something like a mass leak across the pond that would come back to bite their clients back home.
In addition, some nations in Europe are a lot more concerned about privacy both legally and culturally than the US, for obvious historical reasons if nothing else, and they may have stronger laws still.