A forum member for Valvetime.net named tabernumse asked Gabe Newell point-blank in an email:
If you announce Half-Life 3 at E3, I will literally attach a valve to my eyeball, and go around with it for a year, to honor the awesomeness of you and your company.
Thank you. That is all.
To which Gabe responded:
We are not announcing anything at E3. Really. We are not announcing Half-Life 3 or Portal 3 or Left 4 Dead 3. We are going to be showing stuff everyone already knows about (CS:Go, Dota 2, 10' UI, ...).
Just to make sure he wasn't kidding, the site asked for video evidence and another confirmation from Gabe. So yeah, they're not going to show anything at E3, unless it's a bold-faced lie. I wouldn't mind that. Pretty please.