Origin's 'On the House Program' is offering Plants vs. Zombies for free this month. The game is free to download and keep, no string attached - except that you have to install and use EA's digital distribution platform. Last month EA gave Battlefield 1942 away for free, and the month prior it offered Dead Space for free.
EA plans on continuing to release full games, expansions, and more at no cost for the foreseeable future. If you like free stuff and don't mind installing Origin, then you can grab Plants vs. Zombies from the aforementioned link.