The latest game offered through the Origin Games On the House program is Medal of Honor Pacific Assault, meaning anyone with an Origin account is entitled to download the World War II shooter for free (thanks Allen). Here's word on the game, which no longer offers multiplayer support due to the shutdown of GameSpy:

Step into the boots of Marine Private Tom Conlin, as you fight your way through the iconic battles of World War II. Work alone and with the help of squad members to complete missions. As squad members gain experience, they develop their own personalities and fight more efficiently. This first-person-shooter features incredible missions, weapons, and vehicles that put you in the middle of the fight.