Yes, it is actually written into the Berne Convention as the right to quote [1]. And this is not going away at all. You will still be able to quote from articles in other articles, in blog posts, or in online discussions.
The problem is that the right to quote does not cover a mere mechanical aggregation of quotes; the resulting work must still be an original work. This affects primarily news aggregators and search engines (insofar as they quote from press publications).