The original FarmVille shut down permanently on December 31, 2020 — a little over eleven years after it launched.
The direct cause was the end of Adobe Flash. Adobe had announced back in 2017 that it would stop distributing and updating Flash Player at the end of 2020, and major browsers dropped Flash support on the same schedule. Because FarmVille was built entirely on the Flash Player plugin, it became unplayable the moment Flash support ended — there was no realistic way to port a game of that age and complexity to HTML5 in time.
Flash itself was discontinued largely because open web standards (HTML5, CSS3) had become both more capable and dramatically more secure; Flash had a long history of critical vulnerabilities that required constant patching.
While the original Flash-based FarmVille is gone from official servers, the franchise continues through FarmVille 2: Country Escape and FarmVille 3 on mobile. Community-run projects like L.O.S Farms exist to keep the original 2009-era experience playable, using preserved game assets and a reverse-engineered server.