Well, there's only been one new Half-life since, so there's not a whole lot to fill in on :P

Um, I guess in the expansions to the original, you played other characters. In Opposing Force, you played Alan Shepard, a marine who is sent in to Black Mesa but gets caught up. This reveals some extra backstory to the Black Mesa Incident. To a lesser extent, so does Blue Shift, where you play Barny. It's pretty short, though, and there's not a whole lot of new stuff to it.

In Half-life 2, though. . . geeze, it's hard to explain. Basically, you know how the Gman recruits you at the end of HL1? This starts out with him putting you back into service. It's many years later (I think 10, I don't recall), and the world is in ruin. The Combine is in control (they were the controlling force behind the Xen aliens you fight in HL1 - the Xen were enslaved by the Combine.) of the earth, and Martin Breen, the administrator who went unnamed in the first game, is sort of their leader. You're just trying to take them down, prettymuch. There's a really good spoilerific story guide site I could track down if you're interested in the more in-depth parts of the story.