Last year, I was able to divulge a few things around E3 - the nature and title of the 2015 Skylanders game, Fallout 4's special edition, and some other stuff like Uncharted Remastered (even though that was the most obvious thing in the world) and that whole Zombi multiplatform deal. I'm sure there was probably more, but I can't remember.
Edit: Oh, I guess I also heard about that new Nier game: https://twitter.com/Doctor_Cupcakes/status/610725911390846976
Anyway, I'm back to say that I've heard from a couple of sources now that RE7 is happening and will debut at E3. I've heard from one source in the media and another linked with Capcom directly. Both were very adamant that it's happening, but as I'm always very cautious to say, this is a rumour and should be treated as such for now.
I'm doing my best to determine whether or not the rumours are true. For now, Resident Evil 7 is looking more and more likely. Some are saying that the press will get a really good look at it, although I'm not yet sure if this will be a private presentation or not.
Update [10/06/2016]: I have received some additional information regarding its aforementioned showing to the media. One source claims there will be an invite-only presentation behind closed doors for press.