To guess what Half-life 3 is we should look at what the previous half-life games did which made them revolutionary, and which areas they have left to improve.
They pioneered the whole concept of presenting linear scripted sequences around the player without removing their controls or switching the camera away. Revolutionary at the time, but now FPS games pretty much do that by default, and the recent wave of modern military shooters has even made this style of presentation a bit of a cliché and not necessarily a good thing anymore. They're likely to stick with this scripted sequence approach, but the next step of improvements would be for those sequences to adapt more naturally to the player's actions during the script.
The Half-life games also presented their entire narrative in uninterrupted real-time (unless you count loading delays and one moment in the first game where Freeman is knocked out). The next logical step up for them would be to eliminate the loading delays. Or at least hide them well enough that they're not noticeable. Dead Space 2 proves this to be a feasible approach.
Half-life 1 had the scripted sequences, but basically just cloned a bunch of generic scientists and security guards without giving any of them any kind of unique personality or even names, and a small handful of voice actors. Half-life 2 increased the variety of "extra" characters (though they do get a bit repetitive once you've recognized all the faces) and they made several major unique characters and put extra care into their facial animation and acting. But the acting was always a little bit wooden, and aside from Alyx at the end of Episode 2, nobody really goes into any kind of extreme emotions. The logical next step of improvement, then, would be for them to step the acting quality up, and with more accurate facial and motion capture.
There's also AI, which has always been better than average in the Half-Life games but not stellar. There's tons of room for improvement. They seem to like modeling different behaviour types for different aliens, so we'll probably see some more original types of aliens, and better flanking and flushing out tactics by the human(oid) soldier enemies.
And there's physics. HL2's early implementation of Havok was the best physics engine for a long time, but Havok itself and other physics engines have made major improvements since then. Things like the Euphoria engine blending between real-time physics and pre-rendered character animations. Also, we'll probably see DMM (digital molecular matter) physics in use in the next game.
Now the story... I'm not entirely convinced that they actually know where they're going with the story. They're quite likely just making it up as they go, so we'll just have to wait and see if they bring it to conclusion or just choose to leave everything as ambiguous as ever. With how much he's been built up, I feel that any explanation of exactly who the G-Man is, and what his purposes is, will be be a disappointment. They're probably better off leaving us in the dark on most of the story
