Christmas is a holiday that brings people together, so perhaps it should be no surprise that Facebook has become a part of millions of peoples’ Christmas experiences. For the first time in its history, Facebook was the number one most visited website in the United States on both Christmas Eve and Christmas Day this year, according to traffic analyst firm Hitwise today.

That’s worth noting. HitWise reported last year that Facebook was number two behind Google on Christmas. People say that Facebook vs. Google will be the Web’s biggest battle in coming years – but it looks like Facebook has already won the battle for Christmas.

Throughout 2009, Google and Yahoo! Mail were both bigger than Facebook, Hitwise says. Facebook was the most popular search query of the last year across all search engine use by U.S. users, however. It’s a social network’s world these days.

One Christmas gift Facebook users may not have expected: December’s major shift away from Facebook’s initial nature as a privacy-centric social network. Apparently that didn’t slow people down from visiting the site on the holidays.