If you have used Origin with much frequency, you might remember that the EA-owned digital distribution service occasionally gave away free games under the "On the House" label. Today, EA has officially retired the program and will not be offering anymore games for free under that promotion, as they confirmed in a response to Polygon.
The promotion started in 2014 as a way for EA to incentivize players to switch away from Steam and start using Origin more often. The service gave away games like Dead Space, Theme Hospital, Dragon Age: Origins, Mass Effect 2, and most recently Peggle last April, for players to download and keep forever. It is distinct from services like PlayStation Plus or Xbox Games with Gold because there's no subscription access and the games are retained on your account regardless of what you pay for.
The timing around this decision is fairly obvious, as EA's Origin Access Premier launches on July 30. The higher tier of Origin Access means no waiting for any games that eventually come to EA/Origin Access and players can just get access them for $14.99 a month or $99.99 a year. It is likely EA wants to incentivize those services by cutting off free games. Using the link to the On the House promotion now just takes you to a page advertising Origin Access.
Regardless of why, the service is over, so don't expect any games to emerge from EA's vault without giving them some money in return.