Dead Space

Deadspace is an immersive game for many reasons. Most game's user interfaces are non-diegetic, meaning they are completely removed from the fiction in the game. The makers of Deadspace didnt want to have a typical Heads Up Display to tell the payer information, so they built it into the game instead.The interface in Deadspace is 'diegetic', meaning that everything is part of the gameplay, for example, the way we can see the health we have on the back of the character we play as.
The game is also very immersive due to the use of environmental storytelling. In the screenshot below, we are told how to kill the creatures we are attacked by in the game, but not through an immersion breaking tutorial box. The instructions are given to us in the form of bloody writing on the wall, presumably left by someone before we got here. The environmental storytelling here tells us how to kill the enemies, and immerses us further by having us believe there have been other people here.