Half-Life 2 is seriously the best single-player game that there is. None "regular game" really compares to its perfection in all fields. The theme, pacing, gunplay, maps, weapons, enemies, atmosphere, smoothness of source engine, etc. all are so unbelievably well though and executed at it just blows my mind.

My reasons for loving Half-Life 2:
Graphics - The game is bloody gorgeous. Even going back to it now, it looks great. 2004 was kinda the height of the engine wars, with the Cry Engine, Doom 3, and Source all being the newest and shiniest tech. The graphics were very very good and ran well on a wide variety of systems at release.
Immersion: You're right, the Half-Life series have quite generic stories. Where they excel though is in how they tell these stories. They are always first-person, you are always in control. The game never takes you out of it, and thus you are free to immerse yourself fully. The worldbuilding is subtle and while the stories are straightforward you can tell that the writers make an effort to make the setting feel like it has real depth. You feel like you are in a living world.
Atmosphere - The look of a post-alien invasion of Eastern Europe looked hauntingly believable. The art style drew upon classic sci-fi staples (Tripod Stalkers, Zombies, etc.) and made them each unique. Beyond the technical fidelity of the graphics, the art direction is impeccable. Contrasting architectural styles throughout the game contribute to the immersion and story, by showing you the history of the world rather than telling you. The music is also phenomenal
The Gravity Gun - Basically the most powerful weapon in the game was just mundane objects flung at enemies forcefully. Incredibly satisfying to take out a grunt with a radiator. The best game mechanic of all time!
Storytelling - You're never explicitly told exactly what is going on or who the Combine is. You've never explained the motivations of the enigmatic G-Man. You witness the story through Gordon Freeman's eyes and are given tantalizing clues as to the nature of the overall conflict. The camera actually never leaves Gordon Freeman's control the entire game.
Sound Design - The audio is incredible in this game. From the Overwatch voice to Dr. Breen's musings about "Are all of humanity's accomplishments to be nothing more than a thin layer of plastic, sandwiched between the Burgess Shale and an eon's worth of mud?" The power of the gun sounds and the animal-like otherworldly sounds of the Alien gun-ships are just so awesome.

Part of why Half-Life is lauded is that it pioneered this form of storytelling, and it took years for other FPS games to catch up. You have to realize that even up until HL2's release, very few FPS games were doing this. Battlefield and COD were very focused on multiplayer game feel and any single-player they may have had was basically just there to teach you how each gun worked.
Today, FPS full-immersion storytelling is standard. It's what made the Modern Warfare games explode into popularity, it's what made the Crysis and Far Cry games become major franchises (FC1 was released a few months before HL2 btw), and today it's more or less a requirement to include an immersive always-in-character silent-protagonist single-player story in your shooter. Looking back now, HL2 hardly seems anything special, but it would be no real exaggeration to say that it was the game that really established the standard. HL1 popularized it, HL2 reaffirmed it. And games today are still struggling to live up to the example it set.

A lot of its excellence is obfuscated by the fact that many games since have adopted Half-Life 2's great ideas.

Half-Life 2 is seriously the best single-player game that there is. None "regular game" really compares to its perfection in all fields. The theme, pacing, gunplay, maps, weapons, enemies, atmosphere, smoothness of source engine, etc. all are so unbelievably well though and executed at it just blows my mind. My reasons for loving Half-Life 2: Graphics - The game is bloody gorgeous. Even going back to it now, it looks great. 2004 was kinda the height of the engine wars, with the Cry Engine, Doom 3, and Source all being the newest and shiniest tech. The graphics were very very good and ran well on a wide variety of systems at release. Immersion: You're right, the Half-Life series have quite generic stories. Where they excel though is in how they tell these stories. They are always first-person, you are always in control. The game never takes you out of it, and thus you are free to immerse yourself fully. The worldbuilding is subtle and while the stories are straightforward you can tell that the writers make an effort to make the setting feel like it has real depth. You feel like you are in a living world. Atmosphere - The look of a post-alien invasion of Eastern Europe looked hauntingly believable. The art style drew upon classic sci-fi staples (Tripod Stalkers, Zombies, etc.) and made them each unique. Beyond the technical fidelity of the graphics, the art direction is impeccable. Contrasting architectural styles throughout the game contribute to the immersion and story, by showing you the history of the world rather than telling you. The music is also phenomenal The Gravity Gun - Basically the most powerful weapon in the game was just mundane objects flung at enemies forcefully. Incredibly satisfying to take out a grunt with a radiator. The best game mechanic of all time! Storytelling - You're never explicitly told exactly what is going on or who the Combine is. You've never explained the motivations of the enigmatic G-Man. You witness the story through Gordon Freeman's eyes and are given tantalizing clues as to the nature of the overall conflict. The camera actually never leaves Gordon Freeman's control the entire game. Sound Design - The audio is incredible in this game. From the Overwatch voice to Dr. Breen's musings about "Are all of humanity's accomplishments to be nothing more than a thin layer of plastic, sandwiched between the Burgess Shale and an eon's worth of mud?" The power of the gun sounds and the animal-like otherworldly sounds of the Alien gun-ships are just so awesome. Part of why Half-Life is lauded is that it pioneered this form of storytelling, and it took years for other FPS games to catch up. You have to realize that even up until HL2's release, very few FPS games were doing this. Battlefield and COD were very focused on multiplayer game feel and any single-player they may have had was basically just there to teach you how each gun worked. Today, FPS full-immersion storytelling is standard. It's what made the Modern Warfare games explode into popularity, it's what made the Crysis and Far Cry games become major franchises (FC1 was released a few months before HL2 btw), and today it's more or less a requirement to include an immersive always-in-character silent-protagonist single-player story in your shooter. Looking back now, HL2 hardly seems anything special, but it would be no real exaggeration to say that it was the game that really established the standard. HL1 popularized it, HL2 reaffirmed it. And games today are still struggling to live up to the example it set. A lot of its excellence is obfuscated by the fact that many games since have adopted Half-Life 2's great ideas.