As much as I loved Half-Life 2, the first game had the better intro.
The relatively calm, almost soothing, tram ride at the start belied the horror and chaos that would unfold in the near future. It gave the player a look at the scale and inner workings of the Black Mesa Research Facility and made the player feel like a small cog in the larger machine at play there. It made the place feel simultaneously grandiose yet 'lived in', cold and antiseptic yet warm and grungy. Walking the halls after the tram ride was a slice-of-life sensation. You were simply on your way to work, listening in on the idle chit-chat of your colleagues.
It's still one of the most memorable intros I've ever seen. A far cry from the usual bombastic, straight-to-the-action intros one usually sees. Even today, thinking back to the first time I played, I can get chills from hearing that music.