I don't necessarily need to be sold on the "experience" but I'd like for there to be a game compelling enough to make me care

Nintendo: New IP, I would love to see the NX, the new Zelda game on the Wii U and anything Metroid.

Sony: New IP's, more of the PSVR & Games, an improved DS4 controller- improved battery life and better quality analog sticks. Live Gameplay of Gravity Rush 2, Horizon, RIME & Detroit.

MS: New IP's, Live gameplay of Sea of Thieves, Recore, Scalebound & Crackdown 3 SP. Xbox Beta program, More titles in the Game Preview Program-including MS IP's. Below release date.

Any platform: Live gameplay-Mass Effect Andromeda, Dishonored 2, Yooka-Laylee, Doom, Hellblade & Deus Ex: Mankind Divided. =)

I really wanted to hang on for Zelda U but I just couldn't.  I even liked the emulator with the quick saves but I've exhausted their backlog as great as it is.

confirmation that the next Nintendo handheld will launch this year and the next Nintendo home console in 2017.

Saints Row 5, a new Red Dead, inFamous 4, Borderlands 3, Sleeping Dogs 2 (a proper sequel), Watch Dogs 2.

So not much but most titles there are expected to come out every 2 years, so it should be an interesting E3

A 3D Donkey Kong game or Diddy Kong Racing 2!

Keep my modest after insanity that was E3 2015.

Nintendo: Introduce whatever NX is going to be and give a time frame for release.

Sony: Release dates for games like Last Guardian and Horizon.

Obviously happy to see game announcements on top, but for now 2016 is so loaded with games I am content even if little new is shown this year.

-Amazing NX show
-A proper trailer and release date for Zelda
-A new major IP, like Splatoon, for NX
-Reveal of Pikmin 4 (NX exclusive)
-Retro Game
-FS exclusive PS4 title
-RE7 teaser
-The Last Guardian trailer and release date
-FFXV release date
-God of War IV reveal

EDIT:

-Mass Effect Andromeda release date and footage

-TES VI announcement

I think that's about it.

Well primarily I want to hear about the NX from Nintendo and any games possibly going for it.

For games generally I'll probably go with Resident Evil 2 remake news, I'm honestly not expecting a Red Dead Redemption 2 or anything else but if they do I;d love to see a release date and a PC port of the last one.

I'll probably be watching this years PC E3 as well since I liked the one last year. Can't be bothered with any sort of gaming news from MS because they are just releasing for Windows 10 and since I'm not going for that OS I won't be buying anything from them for the foreseeable future until they decide to support their previous OS's or create 11 and make it different from 10 along with supporting Steam. (I honestly really don't care for being lectured on why MS is doing what they are tbh, I just disagree with their stance and vision and since it doesn't appeal to me I'll give my money to someone else until MS supports my own vision).

Golden Sun.

I'm expecting Azure Striker Gunvolt 2 to be there.