I'm not a fan of Facebook, but the movie "The Social Network" was well received by the general public and critics alike. It got a number of movie awards including several Oscar nominations and actually won three of them. I guess it depends on your definition of a classic as it was released in 2010.
I can take or leave Facebook and I realize there are those who enjoyed the movie. But still do not see it as a movie that fits well in a set of classic movies. This is more of a title that should get a separate release IMHO.