When Half-Life came out, it was pretty amazing. If you're in your teens now, you won't be able to appreciate it much.
Essentially what made HL such a good game was the story + gameplay synergy which took a lot of people for quite a ride. Back when it came out, I had a computer that would make anyone blush and scoff, and it did require some pretty decent hardware to run out of what was available (Voodoo was the essential benchmark at the time -- yes I know that term is lost to anyone born in the 90's). So I played at an affluent friend's house and that was one awesome experience. (Obvious point coming) It was like being able to follow a story along with someone else essentially by point-of-view of the character, so you only knew what they knew. At that time, the only games that had story lines were essentially RPGs and you could know quite a bit more about the area, quest, enemies, and weapons than the character you controlled. HL came somewhat out of left field and paved the way for immersive FPS story telling. I was actually quite surprised that it was able to get off the ground because of the graphical resources it required was directed into a small and expensive market.
Now for many people, HL left us with tons of unanswered questions and plot-holes. Essentially at the end of the game everyone went "Uhhhmmmm... okay now...uhhh...right." And pliff. Valve did try and curb this by releasing HL:BS and HL:OF which were pretty awesome as they told the same story from a different perspective VERY well, even if it was to suck the teet of HL's massive success breast.
HL2 came out after a huge development time and essentially filled the boots of its predecessor almost perfectly. It is a subjective opinion, but I thought HL2 was very well done. The whole surreal "what the fuck is going on?" from the beginning of the game is the centre of the game's sub-plot. The primary plot being 'Destory the Combine' (whoever the fuck they are). The story however needed something more, I think. There just wasn't enough answered and more questions added to the finale. Ep1 did little to curb the confusion into conclusion. Ep2 did a better job I think at starting to explain major sub-plots/plot-holes (G-Man) but of course Valve decided to end it right when it was starting to get interesting.
Everyone is getting pissed at the seemingly gigantic production time of Ep3, but you have to admit, it has major shoes to fill and huge answers to give stemming from the original Half-Life. Living a couple blocks away from Valve HQ up here, it seems like they are putting massive effort into closing the rift.
We'll have to see, but I was impressed with both games. The first one more of course, but it was the timing and the thoroughness that made that game what it is.