Tickets have been necessary for visiting the core area since 2013. Per the site FAQs:
From October 2013, Barcelona City Council has got under way a plan for regulation of the monumental zone of Park Güell, with the priority objective of preserving this iconic space of our city and keeping it in the best possible state of conservation. For years now, Park Güell and its entire surrounding area have been suffering from mass tourist visits that involve serious disturbance for local residents, as well as a constant degradation of this architectural heritage, unique in the world. In order to avoid a worsening of that situation, visitor tickets are being regulated, especially to the Monumental Zone, which is the most fragile and densely visited.
The majority of the park is free to access, however the area which houses Gaudí's works (the lizard, curved benches, Hansel and Gretel style houses) have a fixed number of tickets available in (I think) half an hour slot. I went there last July and bought tickets online. Apparently access is free if you live in the neighbourhood.
Here is another article which says core area is ticketed since 2013.