Provided you have the game and an inactive account
Square Enix wants to show off the new content that the latest patch brought to Final Fantasy XIV: A Realm Reborn. Accordingly, account holders who have let their subscription become inactive are able to login for free this weekend.
The free login period runs from Saturday, January 11, 2014 at 12:00 a.m. PST to Monday, January 13, 2014 at 12:00 a.m. PST.
Allowing people whose accounts have lapsed into inactivity come back for a free taste of the new content is a pretty good idea. It's kind of like what drug dealers do.