EA's Origin Access service will get a little more worth it with the addition of Mirror's Edge Catalyst, Star Wars Battlefront, and EA Sports UFC 2, which are all heading to the subscription program later in the year. Need for Speed Most Wanted is also on the way (you can spy it on the Origin 'vault' page), but it's not clear if this will be arriving at around the same time.
Origin Access is the PC's version of (Xbox One subscription program) EA Access, which offers a selection of Origin games, advance trials, and other benefits in exchange for several dollars/pounds a month. Here's a list of all the games included at the moment; it's not enormous, but there are plenty of good and recent titles included.
If you'd like to play a good, not recent EA game in exchange for no money, Dungeon Keeper is currently 'on the house', meaning you can download it now and keep it (the rub is that you have to use Origin).