It's not really a matter of privacy itself being taken more seriously in Europe. It's more a matter of a differing view in the proper role of government. In the U.S., at least traditionally, the proper role of the government has been seen to be more limited than in Europe. While this is perhaps somewhat less true today than 200 years ago, it has still been true to a large degree for the entire existence of the U.S. This includes less government limitations on what contracts private parties (whether individuals, private organizations, or businesses) are allowed to enter into with each other.
Since government limitations on what data Internet companies can store on users (with the permission of the user) is inherently a limitation on what contracts private entities may enter into with each other, the U.S. has been more reluctant than Europe to create such limitations, just as it is with other limitations on private contracts (or private actions in general.)
When it comes to privacy protection from the government, the situation is different. For example, even in a criminal case where all of the standards for a search warrant are met, you cannot be legally compelled to supply a password or encryption key in the U.S., while in Europe you can be so compelled. In the U.S., this is considered a violation of the 5th Amendment, which, among other things, says that you can't be forced to be a witness against yourself. (Edit: As Dan pointed out in the comments, apparently a circuit split now exists with regard to this in the U.S., so the issue will likely end up being addressed by the Supreme Court.)
In addition to the protections granted in the 5th Amendment, the 4th Amendment to the U.S. Constitution states that:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
In general, this bans the government from searching or seizing without your consent any of your property or communications (or yourself) without a warrant showing that you've probably committed or are about to commit a specific crime and specifically describing what can be searched or seized (and this is interpreted by courts to only extend to things which could reasonably by construed to be likely to provide evidence of that specific crime.)