Thief is credited with starting the whole "stealthy" game genre. However, the genre remained pretty subtle until the original Splinter Cell blew open the doors. Splinter Cell is a technical marvel. The animations, the lighting, the unfolding storyline, the lead character Sam Fisher, and the sound all create a hugely compelling and awesome game.
And immersive. The best example of the immersion is when you're creeping along and somebody hears you, or maybe spots some motion in the shadows. At that point, the "other guys" become alert and will start looking around more actively. But here's the kicker: at the point that they become alert, the game issues this sort of "bong!" sound, which then kicks off some suspense-y music. But that initial bong -- you totally tense up and freeze. You stop and listen to what the guard might mutter. You quickly look around to see what is going on; where the guy might be; is he coming your way? But you physically tense up and react.
That is immersion. And it rules.