I think my favorite moment in recent gaming memory was in Fallout 4. My character was still a relatively low level, and was out exploring with Dogmeat in tow. Along the way stumbled upon the ruins of a boarded up church. Entering the church from the basement, you enter into what feels like a scene from a horror movie. There is something big upstairs stomping around, making the floor rattle. It gave me flashbacks to Jurassic Park. We slowly snuck through the church basement, ascending to the next floor, still creeping around, turn a corner and boom, the source of the noise and shaking floors...a deathclaw, who happens to be inhabiting the place and doesn't appreciate that you're interrupting his privacy. It murdered me in a couple blows. I reload back downstairs, and try a few more times to no avail. End up coming back later when I am higher level with better gear and avenging my lowbie self from the past.
For whatever reason, I found that little snippet of Fallout 4 to be extremely immersive. Obviously I knew I wasn't really there, but the game managed to really draw me in, to the point that my my hands were sweating, and my heart was racing.