Question: do you generally like pre-Call of Duty 4 first person shooters? If the answer is no, I wouldn't bother playing further. If the answer is yes, then I would. I always loved the initial flight to Black Mesa East, but a lot of people found it overly drawn out, particularly the hovercraft level. The latter levels are generally more intense, i.e. there's a sense of more stuff going on than you merely running away, and likewise there's a greater variety of weapons, and more interesting set pieces, so it might be worth your while to see them, only if you like this sort of game that is.
In my opinion, Half-Life is about above average shooting mechanics in generally well designed encounters, coupled with exploration of detailed, believable settings, encountering environmental puzzles which have a satisfying logic to them, and experiencing non-expository story telling. What I mean by that last bit is that the game never has a character sit down and explain stuff to you verbally; instead, Valve is one of the few developers to recognize that video games are a visual medium and thus words aren't the only way to tell a story in such a medium. Accordingly, much of the narrative of the game is embedded in the level design: the ruins on the horizon aren't just background decoration, that's a place you're going to visit later; graffiti gives oblique details about another place you visit; an old photograph in a lab establishes otherwise unnoticed connections between characters; etc.
One final note: although I do believe the gameplay elements I just described make the game worthwhile for its own sake, a lot of what made this game so impressive when it came out 10 years ago was the technology. Now granted, game tech progress slowed dramatically starting around 2006 or so, so the difference between a game released today and in 2004 isn't as striking as the difference between a game released in 2004 and another in 1994, but that said, a big part of what made Half-Life 2 such a holy-shit experience a decade ago will no longer impress. I was one of the lucky few to actually successfully activate Half-Life 2 through Steam at midnight on release night, and when the intro with the G-Man got started, I was completely floored by how expressive and real the character animation seemed. Same deal when I met Alyx for the first; a big part of what made her likable for me was simply the fact that she moved and emoted like a person, rather than like a video game character. The graphics were similarly impressive, particularly opening the door on the train station to get your first glimpse of the Citadel. Today, these sorts of things just aren't going to have much impact.
