Square Enix is flipping the switch and letting everyone play Final Fantasy XIV for free on PlayStation 3 until the game’s servers are shut down on June 16, 2017.
The final “Free Login Campaign” for PS3 will start this May 1, 2017 and will last until the service ends. Full details straight from Square Enix can be seen below.
Campaign Schedule
From Monday, May 1, 2017 at 12:01 a.m. (PDT) to Thursday, June 15, 2017 until the start of Stormblood early access maintenance
Eligibility

Users that have registered the PlayStation®3 version of FINAL FANTASY XIV and play using the PlayStation®3
Users with multiple platforms registered to one service account will only be eligible to play for free when logging in from the PlayStation®3
Notes Regarding the Free Login Campaign on PlayStation®3

During the campaign period, players who have only registered the PlayStation®3 version without subscribing for any number of days will be unable to utilize additional services or website related features such as logging into the Lodestone.
In the event players are eligible for multiple campaigns, the number of remaining days displayed will be for the current campaign only.
Service accounts that have been canceled or suspended are not eligible to participate.

Those who play it for free and want to continue the FFXIV goodness, you can upgrade to the PS4 version free of charge via the upgrade campaign.
In accordance with the end of PlayStation®3 service, PlayStation®3 users...