In Crysis (can't remember if they added this to 2 and 3) you don't pick up items, ammo, weapons, etc. by just walking over them, you have to look at them and then pick them up, and you'll actually see your guy's arm shoot out and pick up the object (rather than it just disappearing and then reappearing in your inventory). That, for me, added a TON of immersion to the game. In addition to making it all feel more real and organic, it actually amplified the feeling of you being alone and surrounded on all sides, and you had to fight and scrap your way through everything and scavenge whatever you could to keep alive.
In all of the 'Arkham' games, the way Batman's suit got more torn up as the game went on, and his face began to look more haggard (I think they even had 5 o'clock shadow showing towards the end). It really reminded you that, despite all his abilities and intelligence, he's still a human being who gets tired, beat up, needs to sleep, etc.
In Syndicate, the way that people were referred to as "Consumers", and not population, or people. Really helped sell the world they were creating.
Pretty much the entirety of X-Com: Enemy Unknown. The way that the your lead scientist, engineer, and tactical officer would talk to you throughout the game, being able to name and have Soldiers come from different countries, the 'mystery man' from the council who would talk to you, being able to look in every individual room and see scientists working, engineers building things, soldiers working out, etc. So much of that game added additional immersion that made it that much better.