The Nintendo NX console is now due for release in March 2017. Furthermore it will NOT be announced or present at E3 this year. There will be a separate announcement for the console later this year.
The only playable Nintendo game at this year's E3 will be "Zelda U" and that has also been delayed until 2017 to (probably) coincide with the NX launch.
Links :
http://www.nintendolife.com/news/2016/04/nintendo_nx_will_be_launched_globally_in_march_2017
http://www.nintendolife.com/news/2016/04/the_legend_of_zelda_wii_u_has_been_pushed_back_to_2017_will_release_on_nx_as_well
So, what ARE they going to present at E3? They seem to have nothing other than Zelda and I'd rather not have that spoiled. I guess I can just ignore Nintendo's E3 this year then.
Just goes to show how wrong all those "rumours" were too.