During his Reddit AMA today, Valve president Gabe Newell stated that Valve is—drum roll—developing new videogames. When it came to the inevitable question about Half-Life 3, Newell joked that "the number 3 must not be said," but also confirmed that Valve has at least one singleplayer game in the works, saying "yes" when asked if the company is developing "any fully-fledged single player games."
When asked in a different thread if Valve would ever consider revisiting the Half-Life and Portal universe in a new game, Newell answered in the affirmative. It's not Half-Life 3: Confirmed, but it is Possible Half-Life Related Game: Not Out of the Question.
Outside of that comment, Newell was as vague as usual about Half-Life. Regarding the anonymous source who said Half-Life 3 doesn't exist, he joked: "I personally believe all unidentified anonymous sources on the Internet."
As for what games are being developed by Valve, Newell said little more except that they are, as would be expected, being developed with the Source 2 engine and that VR games are in the works.
"We are continuing to use Source 2 as our primary game development environment," wrote Newell. "Aside from moving Dota 2 to the engine recently, we are are using it as the foundation of some unannounced products. We would like to have everyone working on games here at Valve to eventually be using the same engine. We also intend to continue to make the Source 2 engine work available to the broad developer community as we go, and to make it available free of charge."
In another answer, Newell said that Valve is designing VR games along with a "knuckles controller," which I assume is this prototype from last October. It also sounds like some of Valve's other games, namely Team Fortress 2 and CS:GO, may be moved to Source 2, as Newell said Valve wants everyone working on games at the company to be using it.
When asked about a future Left 4 Dead game, Newell explained that new products at Valve usually come from the combination of new technology, people interested in that technology, and a game property that feels like "a natural playground for that set of technology and design challenges." He called Left 4 Dead "a good place for creating shared narratives." He confirmed nothing, but various leaks have pointed to Left 4 Dead 3 being in development in the past.