Through Origin's Game Time program, it's currently possible to play Plants vs. Zombies: Garden Warfare and Kingdoms of Amalur: Reckoning for free -- for a limited time, of course. Simply download either game and, once you launch it, the clock will begin counting down.
For Garden Warfare, which I cannot recommend enough -- seriously, now's your chance! -- Origin users are getting unlimited access for 72 hours, while Kingdoms of Amalur is restricted to 48 hours of free play. It's unclear how long these offers will remain valid, so I wouldn't wait too long if you're interested. Something to play over the weekend, perhaps.