Officially announced games:

Please note that while EA has confirmed all of these as being at E3, they have not confirmed that all will be up on stage.

Star Wars Battlefront II
FIFA 18
Madden NFL 18 (expect a lot from this due to the new engine and multiple new modes)
NBA LIVE 18
Need For Speed: Payback
The Sims Mobile
The Sims 4
Battlefield 1: In the Name of the Tzar
New content from Star Wars: Galaxy of Heroes
New content for Titanfall 2
Madden NFL Mobile
NBA LIVE Mobile
EA SPORTS FIFA for Nintendo Switch

Teased/rumored games:

Hazelight's new game has been teased for E3. Hazelight is the development team that was behind Brothers: A Tale of Two Sons back when they were at Starbreeze. We saw a preview of it featuring two men on a train.

BioWare's new IP was originally slated to unveil at E3. The game has since been delayed for an unknown amount of time, and it is no longer clear if it will be debuted there.

Additional notes:

EA has an "EA Originals" publishing initiative featuring indie games targeting 3-4 release as year. Known titles for this initiative include Unravel 2, Fe, Sea of Solitude, and the above mentioned Hazelight game. It's plausible they will show more than one title from this branch.

While Visceral's Star Wars game has been in development for quite a while, it's not due to be out until Fall 2018, so don't hold your breath for a new showing unless EA feels they really need more out of their conference.

While Plants vs. Zombies: Garden Warfare 3, Titanfall 3, Respawn's Star Wars game, the next Battlefield, Dragon Age 4, and Motive's new IP open world game all appear to be in development, none of them seem likely to unveil here, so if you're only here for one of those, it's probably not worth it.

EA usually has a segment about their esports division at their event. I can't imagine this year will be any different.

EA will have a 20 vs 20 player Battlefront 2 livestream of the "Assault on Theed" prequel trilogy map featuring your favorite YouTubers, Twitch Streamers, and more. No word on if this will include celebrities on drugs.
Nas and other musical guests will be present for a concert, though I'm not sure if that's part of the livestream.