Gabe Newell, resident boss, God of the PC Master Race, and our Lord and Savior - has answered the question to end all questions: where the f*** is Half-Life 3... well, kinda.
During his recent AMA on Reddit, Newell was asked: "What is the status of Half Life 3/Half Life 2 Episode 3? Is Valve still working on any fully-fledged single player games? An unidentified anonymous source at Valve has said that Half Life 3 has been cancelled. Is that source legitimate?"
Newell's cryptic, but awesome response: "The number 3 must not be said. Yes. I personally believe all unidentified anonymous sources on the Internet".