A recent unnamed insider with Valve has stated simply that if you're waiting for Half-Life 3, stop waiting. Game Informer did an at-length interview with an individual willing to give some background on the game's development, and what we learned was that there isn't any REAL development happening...

"There is no such thing as Half-Life 3. Valve has never announced a Half-Life 3. The closest they’ve come is after Half-Life 2, they said there would be three episodes. We only got two of those. That is arguably an unfulfilled promise. Anything else that we might think about as a full game or sequel has never been promised. I only mention that because it’s sometimes frustrating when people sort of assume or have wishful thinking about the future. Because they want to speak about the future, the fantasy starts to become real in their minds, even though they have a completely different form on the developer side."

Instead, the insider states that Half-Life 3 is little more than a fantasy project that new people to the team or groups occasionally work on. None of these projects collaborate and every time the idea comes to light in the office it's a different team working on something new and always a fresh concept...

"I’ve heard that some teams have had two to three people working on it, and they eventually ran into a wall, and some teams may have gotten up to 30 or 40 people before it was scrapped...They’ve had some different thoughts about what it should be. Some are all over the place, from one end of the spectrum being what you would expect – a single-player narrative-focused game – to completely different entertainment ideas that are as wild as they are weird. They were thinking about using the Half-Life characters as a brand for entirely different purposes. Some were bizarre, like turning Half-Life into an RTS, or a live-action, choice-driven game. These things have been contemplated by people, but were never being considered by the whole of Valve as “Yeah, that was the plan.”

While the insider explicitly states again and again that Half-Life 3 is not a present goal of Valve, nor has it ever been, he doesn't rule out the possibility that the company may one day make a decision to move forward with a project. He still feels that scenario is very doubtful...

"I don’t think there will be any more. But at any given moment, they make decisions as they come. If some people within Valve make something that they collectively feel is exciting, then it will happen. That’s going to be hard for that to happen now. Every time a Half-Life project gets some gravity and then collapses, it becomes harder for the next one to start up."

Seeing as we have no idea who this person is, it's good to take this interview with a healthy bit of skepticism. At the same time, I think what he's saying is making sense, and honestly I don't think Valve has any reason to make Half-Life 3 other than to appease fans. If they were in trouble or needed the money? Sure. Valve isn't in that place right now, and with the success of Steam, I doubt they will be for a long time.