It's been said time and time again that Valve can't count to three. While Half-Life is the series that's most often brought to mind when this is mentioned, it's not just Half-Life 3 that Valve hasn't made; it's also Half-Life 2: Episode 3.
For those who have forgotten (or are too young to remember), Valve actually announced Half-Life 2: Episode 3 10 years ago. It was supposed to release in 2007, but somewhere along the way it was pushed aside and nobody outside of Valve knows why.
Half-Life 2: Episode 3 was first announced on May 24, 2006. As you can see in the video above, Valve was once pretty happy to talk about the impending game and how amazing it was going to be. The holiday 2007 release window drew close, and it became clear the game was going to be delayed; Valve was still talking about it like it was a future project, not a game with an impending release. After the anticipated release window had passed, the company continued talking about the game but became increasingly vague as to when fans might have a chance to play it for themselves.
This lasted until 2009, at which point the game stopped being mentioned entirely. Questions about Half-Life 2: Episode 3 and Half-Life 3 were met with statements about how the company wouldn't comment on the games until it had something to say. Nothing was ever said, however, and now a full decade has passed. Even worse, there is no reason to believe that the game is any closer to release (or even anywhere on the development slate) than it was 10 years ago.
Even if the game is in development, it won't necessarily have the same feel as the previous games. All of the Half-Life games thus far were written by Marc Laidlaw, and he retired from the company earlier this year. While a change in writers is certainly possible, one has to wonder how it would affect the story and how well that story would fit in with the previous entries.
At this point, the prospect of Half-Life 3 being released has become a running joke in the gaming community. Half-Life 2: Episode 3 doesn't even have that distinction, as 10 years on there seems to be very few gamers holding on to the hope that the game will be released anytime soon. Even if it never sees the light of day, though, there's always Left 4 Dead 3, right? Right?