I didn't really get a chance to watch much of E3 live, but I have seen a handful of trailers and such afterwards. There was some interesting stuff in there, so I'll point out what I thought was cool.
The thing I was most looking forward to was Halo Wars 2, which had a pretty awesome trailer. They also announced the beta was playable right now; although it's incredibly buggy, it was pretty fun from what I've played.
Also from the Microsoft conference were ReCore and We Happy Few, which both looked really cool to me. ReCore looks like an awesome sci-fi/wasteland action game, while We Happy Few felt very Bioshock-esque.
Sony announced a new God of War game, but this time Kratos is stuck in the world of Norse Mythology. It looked a lot different from the older games, being a bit slower and more character driven, but the Spartan's brutality and rage are still as awesome as ever.
They also announced remasters of the original Crash Bandicoot trilogy, which sounds amazing. No trailer, though.
There was some stuff on the new South Park game; I thought the Stick of Truth was great, and this one looks to be just as fun.
Trailer, but it's South Park so NSFW:
Bethesda announced the next batch of DLC for Fallout 4 as well as a Skyrim remaster; nothing too earthshattering, but those are two favorites of mine so I was happy to hear about them.
Fallout 4/Fallout Shelter/Skyrim Special Edition: 2016 #BE3 Showcase Presentation
Battlefield 1 continued to look impressive, really interested in trying that one out.
Battlefield 1 Official Gameplay Trailer
I'm probably forgetting some stuff but this is what I could remember off the top of my head. Solid E3 IMO, some good games in there but nothing that really jumped out at me.