There's a stupid myth STILL floating around that EA Access is for sports lovers.. meaning, unless you play sports games - it's a terrible deal. Mostly coming from PS4 players.
Plants vs Zombies - Really popular, tons of people playing. It's very rated G (kids up to adults) but you can be in your 20's/30's and have a lot of fun with it.
Battlefield 4 - I don't think this needs any introduction but the maps are insanely huge. You can fly attack choppers, jets, even the famed Warthog. There's everything from hover craft to tanks. A very large selection of guns, grenades, etc. There's even an absurd amount of knives to collect.
Titanfall - Still feels like the underdog. After going through a quick training tutorial on how to use a giant attack robot, you'll also learn how to take them down. It's important because in each match you'll typically get at least 1 chance to play your titan (giant robot thingy). They deal massive damage and in packs, they can destroy the enemy. You can run on walls with this game, use cards to give certain boosts, etc. It's a lot of fun for everyone from very casual players to more experienced ones.
Dragon Age: Inquisition - Personally, I LOVE this game. I really love the detail, going into castles, fighting huge dragons, the storyline itself. I'm not really into RPG's, but this one got my attention. For me, it has everything one could look for in an a modern day RPG including beautiful weapons and armor upgrades.
Battlefield: Hardline - You'll see a lot of people saying this game should have never been $60. That's absolutely true. It's not even remotely comparable to BF4 but there is fun to be had with it. First off, it's something different.. you're riding around in both cop cars and civilian cars. The storyline for the campaign is much closer to CSI: Miami sorta vibe.. with what are called episodes. I didn't have a problem with the campaign, the story was clear and concise. But again, with the game overall.. not worth $60 but absolutely worth playing with EA Access.
I wont get into the sports games because I hate sports which is ironic some people think that's all EA Access is about.