Brown colour palettes, macho characters that swear too much, first-person cut-scenes, quick-time-events and tonnes of dirt and blood on my camera lens.
Yes, just kidding
Fluid or realistic motion of your character always makes me feel much more connected to the character.
I love in the Arma games that you can independently move your head and your gun -- your mouse will just move your gun until it's moved to some (configurable) threshold value, and then your character's body starts to turn. Also, you can hold alt to just turn your character's head without turning their body. If you're really into it and own a TrackIR (or use free-track), then that increases immersion immensely, as after a while your own head/neck become a direct game peripheral linked to your in-game head/neck.
After playing Arma too much, now when I play other games, I instinctively jerk my head to the side by a few degrees to check my periphery and for a moment wonder why my in-game camera didn't rotate, it's become that natural I wish every FPS supported these devices...
Arma also breaks from FPS tradition of the first-person weapon being drawn over the scene at the end, and instead your entire 3rd-person body is visible in 1st-person mode -- your arms/gun/legs/chest are visible to yourself exactly the same way that they're visible to others. It always annoys me in a regular shooter, say Counter-Strike, where you think you're hidden behind that crate, but to other people, your gun is sticking out around the corner -- there's no way for you to know, because your 1st person view of yourself is completely different to the 3rd person view of yourself that others see, so you never really feel fully connected to the environment.
Unfortunately many of Arma's other animations are really poor and jerky, like jumping over fences, changing stances, or reloading, which all make you feel very disconnected from your character...
Other examples of fluid movement that I love are FarCry 2's crouch-slides, or BF3's vaulting of obstacles -- when you sprint at a concrete barrier and jump over it, you actually see your character place his hand on top of it and see your legs swing over. The camera also bobs the right amount to make you feel like you're actually connected to the world and the character.