I view the story of Half-Life as optional. It's window dressing; very nice, well thought-out window dressing, but not necessary to the enjoyment of the game. The real work was never in the plot of the actual games; it's in the environmental storytelling, like that abandoned house you find during the long drive in HL2, or the really detailed commute to work at the beginning of HL1. It's not an amazing story per se, but it's set in a believable world.
I mean, the story of Half-Life 1 was "Some dudes come through a portal and you shoot them, then the government sends some dudes and you shoot them, then you go through a portal yourself to shoot the biggest dude and win the game". The plot of HL2 was a bit more pretentious, but basically the same (haven't played the episodes yet so I can't speak to those).
The most genius part of the Half-Life story is that it's just vague enough to be interesting, 90% of which comes from G-Man and Gordon Freeman:
- Gordon Freeman has an implied backstory based on how characters interact with him throughout the series, but we never learn any details and Gordon himself never speaks up, so we can fill in just about any personality we like. Bam, intrigue.
- G-Man is a mysterious figure who always seems involved, but never gets his own hands dirty; you see him peering through windows, observing from a distance and manipulating from the shadows, but you never learn what he's doing or where he comes from. Bam, intrigue.
This isn't to demean the story; it was most likely totally intentional that it turned out this way, and a lot of thought was obviously put in to how to present what little information is given to the player. But the story is more interesting for what you have to speculate on, rather than what actually appears in the games.