Update: The trademark entry has disappeared. That means that this is most likely a hoax. So the wait continues.
It’s happening! A keen-eyed user on Neogaf has spotted some Valve trademark filings in Spain (which means that it covers all of the European Union), including the game we’re all dying to see – Half Life 3.
Does this give us any indication on when Half Life 3 will come out? Sort of. When a company registers a trademark in Europe, they have 3-5 years to do something with it (source 1, 2). From there, they can file for short 6 month extensions a few times, after which the trademark would be considered abandoned (source 1, 2, 3).
Valve HAS to do something with the trademark; otherwise, they will lose it. This effectively ends any speculation that they have abandoned the series completely, in favour of gaming hardware and free to play games like DOTA and TF2.